statistical analysis for quantitative research

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organizations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organize and summarize the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalize your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarize your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, other interesting articles.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalize your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

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In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalizable findings, you should use a probability sampling method. Random selection reduces several types of research bias , like sampling bias , and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to at risk for biases like self-selection bias , they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalizing your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalize your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialized, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalized in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardized indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarize them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organizing data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualizing the relationship between two variables using a scatter plot .

By visualizing your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

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The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimize the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasizes null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval

Methodology

• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hostile attribution bias
• Affect heuristic

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Quantitative Data Analysis 101

The lingo, methods and techniques, explained simply.

By: Derek Jansen (MBA)  and Kerryn Warren (PhD) | December 2020

Quantitative data analysis is one of those things that often strikes fear in students. It’s totally understandable – quantitative analysis is a complex topic, full of daunting lingo , like medians, modes, correlation and regression. Suddenly we’re all wishing we’d paid a little more attention in math class…

The good news is that while quantitative data analysis is a mammoth topic, gaining a working understanding of the basics isn’t that hard , even for those of us who avoid numbers and math . In this post, we’ll break quantitative analysis down into simple , bite-sized chunks so you can approach your research with confidence.

Overview: Quantitative Data Analysis 101

• What (exactly) is quantitative data analysis?
• When to use quantitative analysis
• How quantitative analysis works

The two “branches” of quantitative analysis

• Descriptive statistics 101
• Inferential statistics 101
• How to choose the right quantitative methods
• Recap & summary

What is quantitative data analysis?

Despite being a mouthful, quantitative data analysis simply means analysing data that is numbers-based – or data that can be easily “converted” into numbers without losing any meaning.

For example, category-based variables like gender, ethnicity, or native language could all be “converted” into numbers without losing meaning – for example, English could equal 1, French 2, etc.

This contrasts against qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If you’re interested in learning about qualitative analysis, check out our post and video here .

What is quantitative analysis used for?

Quantitative analysis is generally used for three purposes.

• Firstly, it’s used to measure differences between groups . For example, the popularity of different clothing colours or brands.
• Secondly, it’s used to assess relationships between variables . For example, the relationship between weather temperature and voter turnout.
• And third, it’s used to test hypotheses in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine.

Again, this contrasts with qualitative analysis , which can be used to analyse people’s perceptions and feelings about an event or situation. In other words, things that can’t be reduced to numbers.

How does quantitative analysis work?

Well, since quantitative data analysis is all about analysing numbers , it’s no surprise that it involves statistics . Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from pretty basic calculations (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions).

Sounds like gibberish? Don’t worry. We’ll explain all of that in this post. Importantly, you don’t need to be a statistician or math wiz to pull off a good quantitative analysis. We’ll break down all the technical mumbo jumbo in this post.

Need a helping hand?

As I mentioned, quantitative analysis is powered by statistical analysis methods . There are two main “branches” of statistical methods that are used – descriptive statistics and inferential statistics . In your research, you might only use descriptive statistics, or you might use a mix of both , depending on what you’re trying to figure out. In other words, depending on your research questions, aims and objectives . I’ll explain how to choose your methods later.

So, what are descriptive and inferential statistics?

Well, before I can explain that, we need to take a quick detour to explain some lingo. To understand the difference between these two branches of statistics, you need to understand two important words. These words are population and sample .

First up, population . In statistics, the population is the entire group of people (or animals or organisations or whatever) that you’re interested in researching. For example, if you were interested in researching Tesla owners in the US, then the population would be all Tesla owners in the US.

However, it’s extremely unlikely that you’re going to be able to interview or survey every single Tesla owner in the US. Realistically, you’ll likely only get access to a few hundred, or maybe a few thousand owners using an online survey. This smaller group of accessible people whose data you actually collect is called your sample .

So, to recap – the population is the entire group of people you’re interested in, and the sample is the subset of the population that you can actually get access to. In other words, the population is the full chocolate cake , whereas the sample is a slice of that cake.

So, why is this sample-population thing important?

Well, descriptive statistics focus on describing the sample , while inferential statistics aim to make predictions about the population, based on the findings within the sample. In other words, we use one group of statistical methods – descriptive statistics – to investigate the slice of cake, and another group of methods – inferential statistics – to draw conclusions about the entire cake. There I go with the cake analogy again…

With that out the way, let’s take a closer look at each of these branches in more detail.

Branch 1: Descriptive Statistics

Descriptive statistics serve a simple but critically important role in your research – to describe your data set – hence the name. In other words, they help you understand the details of your sample . Unlike inferential statistics (which we’ll get to soon), descriptive statistics don’t aim to make inferences or predictions about the entire population – they’re purely interested in the details of your specific sample .

When you’re writing up your analysis, descriptive statistics are the first set of stats you’ll cover, before moving on to inferential statistics. But, that said, depending on your research objectives and research questions , they may be the only type of statistics you use. We’ll explore that a little later.

So, what kind of statistics are usually covered in this section?

Some common statistical tests used in this branch include the following:

• Mean – this is simply the mathematical average of a range of numbers.
• Median – this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers.
• Mode – this is simply the most commonly occurring number in the data set.
• In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low.
• Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high.
• Skewness . As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right?

Feeling a bit confused? Let’s look at a practical example using a small data set.

On the left-hand side is the data set. This details the bodyweight of a sample of 10 people. On the right-hand side, we have the descriptive statistics. Let’s take a look at each of them.

First, we can see that the mean weight is 72.4 kilograms. In other words, the average weight across the sample is 72.4 kilograms. Straightforward.

Next, we can see that the median is very similar to the mean (the average). This suggests that this data set has a reasonably symmetrical distribution (in other words, a relatively smooth, centred distribution of weights, clustered towards the centre).

In terms of the mode , there is no mode in this data set. This is because each number is present only once and so there cannot be a “most common number”. If there were two people who were both 65 kilograms, for example, then the mode would be 65.

Next up is the standard deviation . 10.6 indicates that there’s quite a wide spread of numbers. We can see this quite easily by looking at the numbers themselves, which range from 55 to 90, which is quite a stretch from the mean of 72.4.

And lastly, the skewness of -0.2 tells us that the data is very slightly negatively skewed. This makes sense since the mean and the median are slightly different.

As you can see, these descriptive statistics give us some useful insight into the data set. Of course, this is a very small data set (only 10 records), so we can’t read into these statistics too much. Also, keep in mind that this is not a list of all possible descriptive statistics – just the most common ones.

But why do all of these numbers matter?

While these descriptive statistics are all fairly basic, they’re important for a few reasons:

• Firstly, they help you get both a macro and micro-level view of your data. In other words, they help you understand both the big picture and the finer details.
• Secondly, they help you spot potential errors in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data.
• And lastly, these descriptive statistics help inform which inferential statistical techniques you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data.

Simply put, descriptive statistics are really important , even though the statistical techniques used are fairly basic. All too often at Grad Coach, we see students skimming over the descriptives in their eagerness to get to the more exciting inferential methods, and then landing up with some very flawed results.

Don’t be a sucker – give your descriptive statistics the love and attention they deserve!

Branch 2: Inferential Statistics

As I mentioned, while descriptive statistics are all about the details of your specific data set – your sample – inferential statistics aim to make inferences about the population . In other words, you’ll use inferential statistics to make predictions about what you’d expect to find in the full population.

What kind of predictions, you ask? Well, there are two common types of predictions that researchers try to make using inferential stats:

• Firstly, predictions about differences between groups – for example, height differences between children grouped by their favourite meal or gender.
• And secondly, relationships between variables – for example, the relationship between body weight and the number of hours a week a person does yoga.

In other words, inferential statistics (when done correctly), allow you to connect the dots and make predictions about what you expect to see in the real world population, based on what you observe in your sample data. For this reason, inferential statistics are used for hypothesis testing – in other words, to test hypotheses that predict changes or differences.

Of course, when you’re working with inferential statistics, the composition of your sample is really important. In other words, if your sample doesn’t accurately represent the population you’re researching, then your findings won’t necessarily be very useful.

For example, if your population of interest is a mix of 50% male and 50% female , but your sample is 80% male , you can’t make inferences about the population based on your sample, since it’s not representative. This area of statistics is called sampling, but we won’t go down that rabbit hole here (it’s a deep one!) – we’ll save that for another post .

What statistics are usually used in this branch?

There are many, many different statistical analysis methods within the inferential branch and it’d be impossible for us to discuss them all here. So we’ll just take a look at some of the most common inferential statistical methods so that you have a solid starting point.

First up are T-Tests . T-tests compare the means (the averages) of two groups of data to assess whether they’re statistically significantly different. In other words, do they have significantly different means, standard deviations and skewness.

This type of testing is very useful for understanding just how similar or different two groups of data are. For example, you might want to compare the mean blood pressure between two groups of people – one that has taken a new medication and one that hasn’t – to assess whether they are significantly different.

Kicking things up a level, we have ANOVA, which stands for “analysis of variance”. This test is similar to a T-test in that it compares the means of various groups, but ANOVA allows you to analyse multiple groups , not just two groups So it’s basically a t-test on steroids…

Next, we have correlation analysis . This type of analysis assesses the relationship between two variables. In other words, if one variable increases, does the other variable also increase, decrease or stay the same. For example, if the average temperature goes up, do average ice creams sales increase too? We’d expect some sort of relationship between these two variables intuitively , but correlation analysis allows us to measure that relationship scientifically .

Lastly, we have regression analysis – this is quite similar to correlation in that it assesses the relationship between variables, but it goes a step further to understand cause and effect between variables, not just whether they move together. In other words, does the one variable actually cause the other one to move, or do they just happen to move together naturally thanks to another force? Just because two variables correlate doesn’t necessarily mean that one causes the other.

Stats overload…

I hear you. To make this all a little more tangible, let’s take a look at an example of a correlation in action.

Here’s a scatter plot demonstrating the correlation (relationship) between weight and height. Intuitively, we’d expect there to be some relationship between these two variables, which is what we see in this scatter plot. In other words, the results tend to cluster together in a diagonal line from bottom left to top right.

As I mentioned, these are are just a handful of inferential techniques – there are many, many more. Importantly, each statistical method has its own assumptions and limitations.

For example, some methods only work with normally distributed (parametric) data, while other methods are designed specifically for non-parametric data. And that’s exactly why descriptive statistics are so important – they’re the first step to knowing which inferential techniques you can and can’t use.

How to choose the right analysis method

To choose the right statistical methods, you need to think about two important factors :

• The type of quantitative data you have (specifically, level of measurement and the shape of the data). And,
• Your research questions and hypotheses

Let’s take a closer look at each of these.

Factor 1 – Data type

The first thing you need to consider is the type of data you’ve collected (or the type of data you will collect). By data types, I’m referring to the four levels of measurement – namely, nominal, ordinal, interval and ratio. If you’re not familiar with this lingo, check out the video below.

Why does this matter?

Well, because different statistical methods and techniques require different types of data. This is one of the “assumptions” I mentioned earlier – every method has its assumptions regarding the type of data.

For example, some techniques work with categorical data (for example, yes/no type questions, or gender or ethnicity), while others work with continuous numerical data (for example, age, weight or income) – and, of course, some work with multiple data types.

If you try to use a statistical method that doesn’t support the data type you have, your results will be largely meaningless . So, make sure that you have a clear understanding of what types of data you’ve collected (or will collect). Once you have this, you can then check which statistical methods would support your data types here .

If you haven’t collected your data yet, you can work in reverse and look at which statistical method would give you the most useful insights, and then design your data collection strategy to collect the correct data types.

Another important factor to consider is the shape of your data . Specifically, does it have a normal distribution (in other words, is it a bell-shaped curve, centred in the middle) or is it very skewed to the left or the right? Again, different statistical techniques work for different shapes of data – some are designed for symmetrical data while others are designed for skewed data.

This is another reminder of why descriptive statistics are so important – they tell you all about the shape of your data.

Factor 2: Your research questions

The next thing you need to consider is your specific research questions, as well as your hypotheses (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use.

If you’re just interested in understanding the attributes of your sample (as opposed to the entire population), then descriptive statistics are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people.

On the other hand, if you aim to understand differences between groups or relationships between variables and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics and inferential statistics.

So, it’s really important to get very clear about your research aims and research questions, as well your hypotheses – before you start looking at which statistical techniques to use.

Never shoehorn a specific statistical technique into your research just because you like it or have some experience with it. Your choice of methods must align with all the factors we’ve covered here.

Time to recap…

You’re still with me? That’s impressive. We’ve covered a lot of ground here, so let’s recap on the key points:

• Quantitative data analysis is all about  analysing number-based data  (which includes categorical and numerical data) using various statistical techniques.
• The two main  branches  of statistics are  descriptive statistics  and  inferential statistics . Descriptives describe your sample, whereas inferentials make predictions about what you’ll find in the population.
• Common  descriptive statistical methods include  mean  (average),  median , standard  deviation  and  skewness .
• Common  inferential statistical methods include  t-tests ,  ANOVA ,  correlation  and  regression  analysis.
• To choose the right statistical methods and techniques, you need to consider the  type of data you’re working with , as well as your  research questions  and hypotheses.

Psst… there’s more (for free)

This post is part of our dissertation mini-course, which covers everything you need to get started with your dissertation, thesis or research project. 

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Quantitative Data Analysis: A Comprehensive Guide

By: Ofem Eteng Published: May 18, 2022

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A healthcare giant successfully introduces the most effective drug dosage through rigorous statistical modeling, saving countless lives. A marketing team predicts consumer trends with uncanny accuracy, tailoring campaigns for maximum impact.

Table of Contents

These trends and dosages are not just any numbers but are a result of meticulous quantitative data analysis. Quantitative data analysis offers a robust framework for understanding complex phenomena, evaluating hypotheses, and predicting future outcomes.

In this blog, we’ll walk through the concept of quantitative data analysis, the steps required, its advantages, and the methods and techniques that are used in this analysis. Read on!

What is Quantitative Data Analysis?

Quantitative data analysis is a systematic process of examining, interpreting, and drawing meaningful conclusions from numerical data. It involves the application of statistical methods, mathematical models, and computational techniques to understand patterns, relationships, and trends within datasets.

Quantitative data analysis methods typically work with algorithms, mathematical analysis tools, and software to gain insights from the data, answering questions such as how many, how often, and how much. Data for quantitative data analysis is usually collected from close-ended surveys, questionnaires, polls, etc. The data can also be obtained from sales figures, email click-through rates, number of website visitors, and percentage revenue increase. 

Quantitative Data Analysis vs Qualitative Data Analysis

When we talk about data, we directly think about the pattern, the relationship, and the connection between the datasets – analyzing the data in short. Therefore when it comes to data analysis, there are broadly two types – Quantitative Data Analysis and Qualitative Data Analysis.

Quantitative data analysis revolves around numerical data and statistics, which are suitable for functions that can be counted or measured. In contrast, qualitative data analysis includes description and subjective information – for things that can be observed but not measured.

Let us differentiate between Quantitative Data Analysis and Quantitative Data Analysis for a better understanding.

Data Preparation Steps for Quantitative Data Analysis

Quantitative data has to be gathered and cleaned before proceeding to the stage of analyzing it. Below are the steps to prepare a data before quantitative research analysis:

• Step 1: Data Collection

Before beginning the analysis process, you need data. Data can be collected through rigorous quantitative research, which includes methods such as interviews, focus groups, surveys, and questionnaires.

• Step 2: Data Cleaning

Once the data is collected, begin the data cleaning process by scanning through the entire data for duplicates, errors, and omissions. Keep a close eye for outliers (data points that are significantly different from the majority of the dataset) because they can skew your analysis results if they are not removed.

This data-cleaning process ensures data accuracy, consistency and relevancy before analysis.

• Step 3: Data Analysis and Interpretation

Now that you have collected and cleaned your data, it is now time to carry out the quantitative analysis. There are two methods of quantitative data analysis, which we will discuss in the next section.

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Now that you are familiar with what quantitative data analysis is and how to prepare your data for analysis, the focus will shift to the purpose of this article, which is to describe the methods and techniques of quantitative data analysis.

Methods and Techniques of Quantitative Data Analysis

Quantitative data analysis employs two techniques to extract meaningful insights from datasets, broadly. The first method is descriptive statistics, which summarizes and portrays essential features of a dataset, such as mean, median, and standard deviation.

Inferential statistics, the second method, extrapolates insights and predictions from a sample dataset to make broader inferences about an entire population, such as hypothesis testing and regression analysis.

An in-depth explanation of both the methods is provided below:

• Descriptive Statistics
• Inferential Statistics

1) Descriptive Statistics

Descriptive statistics as the name implies is used to describe a dataset. It helps understand the details of your data by summarizing it and finding patterns from the specific data sample. They provide absolute numbers obtained from a sample but do not necessarily explain the rationale behind the numbers and are mostly used for analyzing single variables. The methods used in descriptive statistics include: 

• Mean:   This calculates the numerical average of a set of values.
• Median: This is used to get the midpoint of a set of values when the numbers are arranged in numerical order.
• Mode: This is used to find the most commonly occurring value in a dataset.
• Percentage: This is used to express how a value or group of respondents within the data relates to a larger group of respondents.
• Frequency: This indicates the number of times a value is found.
• Range: This shows the highest and lowest values in a dataset.
• Standard Deviation: This is used to indicate how dispersed a range of numbers is, meaning, it shows how close all the numbers are to the mean.
• Skewness: It indicates how symmetrical a range of numbers is, showing if they cluster into a smooth bell curve shape in the middle of the graph or if they skew towards the left or right.

2) Inferential Statistics

In quantitative analysis, the expectation is to turn raw numbers into meaningful insight using numerical values, and descriptive statistics is all about explaining details of a specific dataset using numbers, but it does not explain the motives behind the numbers; hence, a need for further analysis using inferential statistics.

Inferential statistics aim to make predictions or highlight possible outcomes from the analyzed data obtained from descriptive statistics. They are used to generalize results and make predictions between groups, show relationships that exist between multiple variables, and are used for hypothesis testing that predicts changes or differences.

There are various statistical analysis methods used within inferential statistics; a few are discussed below.

• Cross Tabulations: Cross tabulation or crosstab is used to show the relationship that exists between two variables and is often used to compare results by demographic groups. It uses a basic tabular form to draw inferences between different data sets and contains data that is mutually exclusive or has some connection with each other. Crosstabs help understand the nuances of a dataset and factors that may influence a data point.
• Regression Analysis: Regression analysis estimates the relationship between a set of variables. It shows the correlation between a dependent variable (the variable or outcome you want to measure or predict) and any number of independent variables (factors that may impact the dependent variable). Therefore, the purpose of the regression analysis is to estimate how one or more variables might affect a dependent variable to identify trends and patterns to make predictions and forecast possible future trends. There are many types of regression analysis, and the model you choose will be determined by the type of data you have for the dependent variable. The types of regression analysis include linear regression, non-linear regression, binary logistic regression, etc.
• Monte Carlo Simulation: Monte Carlo simulation, also known as the Monte Carlo method, is a computerized technique of generating models of possible outcomes and showing their probability distributions. It considers a range of possible outcomes and then tries to calculate how likely each outcome will occur. Data analysts use it to perform advanced risk analyses to help forecast future events and make decisions accordingly.
• Analysis of Variance (ANOVA): This is used to test the extent to which two or more groups differ from each other. It compares the mean of various groups and allows the analysis of multiple groups.
• Factor Analysis:   A large number of variables can be reduced into a smaller number of factors using the factor analysis technique. It works on the principle that multiple separate observable variables correlate with each other because they are all associated with an underlying construct. It helps in reducing large datasets into smaller, more manageable samples.
• Cohort Analysis: Cohort analysis can be defined as a subset of behavioral analytics that operates from data taken from a given dataset. Rather than looking at all users as one unit, cohort analysis breaks down data into related groups for analysis, where these groups or cohorts usually have common characteristics or similarities within a defined period.
• MaxDiff Analysis: This is a quantitative data analysis method that is used to gauge customers’ preferences for purchase and what parameters rank higher than the others in the process. 
• Cluster Analysis: Cluster analysis is a technique used to identify structures within a dataset. Cluster analysis aims to be able to sort different data points into groups that are internally similar and externally different; that is, data points within a cluster will look like each other and different from data points in other clusters.
• Time Series Analysis: This is a statistical analytic technique used to identify trends and cycles over time. It is simply the measurement of the same variables at different times, like weekly and monthly email sign-ups, to uncover trends, seasonality, and cyclic patterns. By doing this, the data analyst can forecast how variables of interest may fluctuate in the future. 
• SWOT analysis: This is a quantitative data analysis method that assigns numerical values to indicate strengths, weaknesses, opportunities, and threats of an organization, product, or service to show a clearer picture of competition to foster better business strategies

How to Choose the Right Method for your Analysis?

Choosing between Descriptive Statistics or Inferential Statistics can be often confusing. You should consider the following factors before choosing the right method for your quantitative data analysis:

1. Type of Data

The first consideration in data analysis is understanding the type of data you have. Different statistical methods have specific requirements based on these data types, and using the wrong method can render results meaningless. The choice of statistical method should align with the nature and distribution of your data to ensure meaningful and accurate analysis.

2. Your Research Questions

When deciding on statistical methods, it’s crucial to align them with your specific research questions and hypotheses. The nature of your questions will influence whether descriptive statistics alone, which reveal sample attributes, are sufficient or if you need both descriptive and inferential statistics to understand group differences or relationships between variables and make population inferences.

Pros and Cons of Quantitative Data Analysis

1. Objectivity and Generalizability:

• Quantitative data analysis offers objective, numerical measurements, minimizing bias and personal interpretation.
• Results can often be generalized to larger populations, making them applicable to broader contexts.

Example: A study using quantitative data analysis to measure student test scores can objectively compare performance across different schools and demographics, leading to generalizable insights about educational strategies.

2. Precision and Efficiency:

• Statistical methods provide precise numerical results, allowing for accurate comparisons and prediction.
• Large datasets can be analyzed efficiently with the help of computer software, saving time and resources.

Example: A marketing team can use quantitative data analysis to precisely track click-through rates and conversion rates on different ad campaigns, quickly identifying the most effective strategies for maximizing customer engagement.

3. Identification of Patterns and Relationships:

• Statistical techniques reveal hidden patterns and relationships between variables that might not be apparent through observation alone.
• This can lead to new insights and understanding of complex phenomena.

Example: A medical researcher can use quantitative analysis to pinpoint correlations between lifestyle factors and disease risk, aiding in the development of prevention strategies.

1. Limited Scope:

• Quantitative analysis focuses on quantifiable aspects of a phenomenon ,  potentially overlooking important qualitative nuances, such as emotions, motivations, or cultural contexts.

Example: A survey measuring customer satisfaction with numerical ratings might miss key insights about the underlying reasons for their satisfaction or dissatisfaction, which could be better captured through open-ended feedback.

2. Oversimplification:

• Reducing complex phenomena to numerical data can lead to oversimplification and a loss of richness in understanding.

Example: Analyzing employee productivity solely through quantitative metrics like hours worked or tasks completed might not account for factors like creativity, collaboration, or problem-solving skills, which are crucial for overall performance.

3. Potential for Misinterpretation:

• Statistical results can be misinterpreted if not analyzed carefully and with appropriate expertise.
• The choice of statistical methods and assumptions can significantly influence results.

This blog discusses the steps, methods, and techniques of quantitative data analysis. It also gives insights into the methods of data collection, the type of data one should work with, and the pros and cons of such analysis.

Gain a better understanding of data analysis with these essential reads:

• Data Analysis and Modeling: 4 Critical Differences
• Exploratory Data Analysis Simplified 101
• 25 Best Data Analysis Tools in 2024

Carrying out successful data analysis requires prepping the data and making it analysis-ready. That is where Hevo steps in.

Want to give Hevo a try? Sign Up for a 14-day free trial and experience the feature-rich Hevo suite first hand. You may also have a look at the amazing Hevo price , which will assist you in selecting the best plan for your requirements.

Share your experience of understanding Quantitative Data Analysis in the comment section below! We would love to hear your thoughts.

Ofem is a freelance writer specializing in data-related topics, who has expertise in translating complex concepts. With a focus on data science, analytics, and emerging technologies.

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Handbook of Research Methods in Health Social Sciences pp 955–969 Cite as

Data Analysis in Quantitative Research

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Quantitative data analysis serves as part of an essential process of evidence-making in health and social sciences. It is adopted for any types of research question and design whether it is descriptive, explanatory, or causal. However, compared with qualitative counterpart, quantitative data analysis has less flexibility. Conducting quantitative data analysis requires a prerequisite understanding of the statistical knowledge and skills. It also requires rigor in the choice of appropriate analysis model and the interpretation of the analysis outcomes. Basically, the choice of appropriate analysis techniques is determined by the type of research question and the nature of the data. In addition, different analysis techniques require different assumptions of data. This chapter provides introductory guides for readers to assist them with their informed decision-making in choosing the correct analysis models. To this end, it begins with discussion of the levels of measure: nominal, ordinal, and scale. Some commonly used analysis techniques in univariate, bivariate, and multivariate data analysis are presented for practical examples. Example analysis outcomes are produced by the use of SPSS (Statistical Package for Social Sciences).

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Jung, Y.M. (2019). Data Analysis in Quantitative Research. In: Liamputtong, P. (eds) Handbook of Research Methods in Health Social Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-10-5251-4_109

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Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

• Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
• Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
• Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
• Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
• Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

• Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
• Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
• Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
• Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
• Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
• Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
• Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

• Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
• Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
• Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
• Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
• Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
• Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
• Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

• Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
• Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
• Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
• Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
• Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
• Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

• To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
• To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
• To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
• To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
• To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

• Description : To provide a detailed and accurate description of a particular phenomenon or population.
• Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
• Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
• Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

• Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
• Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
• Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
• Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
• Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
• Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

• Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
• Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
• Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
• Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
• Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
• Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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What Is Statistical Analysis? Definition, Types, and Jobs

Statistical analytics is a high demand career with great benefits. Learn how you can apply your statistical and data science skills to this growing field.

Statistical analysis is the process of collecting large volumes of data and then using statistics and other data analysis techniques to identify trends, patterns, and insights. If you're a whiz at data and statistics, statistical analysis could be a great career match for you. The rise of big data, machine learning, and technology in our society has created a high demand for statistical analysts, and it's an exciting time to develop these skills and find a job you love. In this article, you'll learn more about statistical analysis, including its definition, different types of it, how it's done, and jobs that use it. At the end, you'll also explore suggested cost-effective courses than can help you gain greater knowledge of both statistical and data analytics.

Statistical analysis definition

Statistical analysis is the process of collecting and analyzing large volumes of data in order to identify trends and develop valuable insights.

In the professional world, statistical analysts take raw data and find correlations between variables to reveal patterns and trends to relevant stakeholders. Working in a wide range of different fields, statistical analysts are responsible for new scientific discoveries, improving the health of our communities, and guiding business decisions.

Types of statistical analysis

There are two main types of statistical analysis: descriptive and inferential. As a statistical analyst, you'll likely use both types in your daily work to ensure that data is both clearly communicated to others and that it's used effectively to develop actionable insights. At a glance, here's what you need to know about both types of statistical analysis:

Descriptive statistical analysis

Descriptive statistics summarizes the information within a data set without drawing conclusions about its contents. For example, if a business gave you a book of its expenses and you summarized the percentage of money it spent on different categories of items, then you would be performing a form of descriptive statistics.

When performing descriptive statistics, you will often use data visualization to present information in the form of graphs, tables, and charts to clearly convey it to others in an understandable format. Typically, leaders in a company or organization will then use this data to guide their decision making going forward.

Inferential statistical analysis

Inferential statistics takes the results of descriptive statistics one step further by drawing conclusions from the data and then making recommendations. For example, instead of only summarizing the business's expenses, you might go on to recommend in which areas to reduce spending and suggest an alternative budget.

Inferential statistical analysis is often used by businesses to inform company decisions and in scientific research to find new relationships between variables. 

Statistical analyst duties

Statistical analysts focus on making large sets of data understandable to a more general audience. In effect, you'll use your math and data skills to translate big numbers into easily digestible graphs, charts, and summaries for key decision makers within businesses and other organizations. Typical job responsibilities of statistical analysts include:

Extracting and organizing large sets of raw data

Determining which data is relevant and which should be excluded

Developing new data collection strategies

Meeting with clients and professionals to review data analysis plans

Creating data reports and easily understandable representations of the data

Presenting data

Interpreting data results

Creating recommendations for a company or other organizations

Your job responsibilities will differ depending on whether you work for a federal agency, a private company, or another business sector. Many industries need statistical analysts, so exploring your passions and seeing how you can best apply your data skills can be exciting. 

Statistical analysis skills

Because most of your job responsibilities will likely focus on data and statistical analysis, mathematical skills are crucial. High-level math skills can help you fact-check your work and create strategies to analyze the data, even if you use software for many computations. When honing in on your mathematical skills, focusing on statistics—specifically statistics with large data sets—can help set you apart when searching for job opportunities. Competency with computer software and learning new platforms will also help you excel in more advanced positions and put you in high demand.

Data analytics , problem-solving, and critical thinking are vital skills to help you determine the data set’s true meaning and bigger picture. Often, large data sets may not represent what they appear on the surface. To get to the bottom of things, you'll need to think critically about factors that may influence the data set, create an informed analysis plan, and parse out bias to identify insightful trends. 

To excel in the workplace, you'll need to hone your database management skills, keep up to date on statistical methodology, and continually improve your research skills. These skills take time to build, so starting with introductory courses and having patience while you build skills is important.

Common software used in statistical analytics jobs

Statistical analysis often involves computations using big data that is too large to compute by hand. The good news is that many kinds of statistical software have been developed to help analyze data effectively and efficiently. Gaining mastery over this statistical software can make you look attractive to employers and allow you to work on more complex projects. 

Statistical software is beneficial for both descriptive and inferential statistics. You can use it to generate charts and graphs or perform computations to draw conclusions and inferences from the data. While the type of statistical software you will use will depend on your employer, common software used include:

Read more: The 7 Data Analysis Software You Need to Know

Pathways to a career in statistical analytics

Many paths to becoming a statistical analyst exist, but most jobs in this field require a bachelor’s degree. Employers will typically look for a degree in an area that focuses on math, computer science, statistics, or data science to ensure you have the skills needed for the job. If your bachelor’s degree is in another field, gaining experience through entry-level data entry jobs can help get your foot in the door. Many employers look for work experience in related careers such as being a research assistant, data manager, or intern in the field.

Earning a graduate degree in statistical analytics or a related field can also help you stand out on your resume and demonstrate a deep knowledge of the skills needed to perform the job successfully. Generally, employers focus more on making sure you have the mathematical and data analysis skills required to perform complex statistical analytics on its data. After all, you will be helping them to make decisions, so they want to feel confident in your ability to advise them in the right direction.

Read more: Your Guide to a Career as a Statistician—What to Expect

How much do statistical analytics professionals earn? 

Statistical analysts earn well above the national average and enjoy many benefits on the job. There are many careers utilizing statistical analytics, so comparing salaries can help determine if the job benefits align with your expectations.

Median annual salary: $113,990

Job outlook for 2022 to 2032: 23% [ 1 ]

Data scientist

Median annual salary: $103,500

Job outlook for 2022 to 2032: 35% [ 2 ]

Financial risk specialist

Median annual salary: $102,120

Job outlook for 2022 to 2032: 8% [ 3 ]

Investment analyst

Median annual salary: $95,080

Operational research analyst

Median annual salary: $85,720

Job outlook for 2022 to 2032: 23% [ 4 ]

Market research analyst

Median annual salary: $68,230

Job outlook for 2022 to 2032: 13% [ 5 ]

Statistician

Median annual salary: $99,960

Job outlook for 2022 to 2032: 30% [ 6 ]

Read more: How Much Do Statisticians Make? Your 2022 Statistician Salary Guide

Statistical analysis job outlook

Jobs that use statistical analysis have a positive outlook for the foreseeable future.

According to the US Bureau of Labor Statistics (BLS), the number of jobs for mathematicians and statisticians is projected to grow by 30 percent between 2022 and 2032, adding an average of 3,500 new jobs each year throughout the decade [ 6 ].

As we create more ways to collect data worldwide, there will be an increased need for people able to analyze and make sense of the data.

Ready to take the next step in your career?

Statistical analytics could be an excellent career match for those with an affinity for math, data, and problem-solving. Here are some popular courses to consider as you prepare for a career in statistical analysis:

Learn fundamental processes and tools with Google's Data Analytics Professional Certificate . You'll learn how to process and analyze data, use key analysis tools, apply R programming, and create visualizations that can inform key business decisions.

Grow your comfort using R with Duke University's Data Analysis with R Specialization . Statistical analysts commonly use R for testing, modeling, and analysis. Here, you'll learn and practice those processes.

Apply statistical analysis with Rice University's Business Statistics and Analysis Specialization . Contextualize your technical and analytical skills by using them to solve business problems and complete a hands-on Capstone Project to demonstrate your knowledge.

Article sources

US Bureau of Labor Statistics. " Occupational Outlook Handbook: Actuaries , https://www.bls.gov/ooh/math/actuaries.htm." Accessed November 21, 2023.

US Bureau of Labor Statistics. " Occupational Outlook Handbook: Data Scientists , https://www.bls.gov/ooh/math/data-scientists.htm." Accessed Accessed November 21, 2023.

US Bureau of Labor Statistics. " Occupational Outlook Handbook: Financial Analysts , https://www.bls.gov/ooh/business-and-financial/financial-analysts.htm." Accessed Accessed November 21, 2023.

US Bureau of Labor Statistics. " Occupational Outlook Handbook: Operations Research Analysts , https://www.bls.gov/ooh/math/operations-research-analysts.htm." Accessed Accessed November 21, 2023.

US Bureau of Labor Statistics. " Occupational Outlook Handbook: Market Research Analyst , https://www.bls.gov/ooh/business-and-financial/market-research-analysts.htm." Accessed Accessed November 21, 2023.

US Bureau of Labor Statistics. " Occupational Outlook Handbook: Mathematicians and Statisticians , https://www.bls.gov/ooh/math/mathematicians-and-statisticians.htm." Accessed Accessed November 21, 2023.

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14 Quantitative analysis: Descriptive statistics

Numeric data collected in a research project can be analysed quantitatively using statistical tools in two different ways. Descriptive analysis refers to statistically describing, aggregating, and presenting the constructs of interest or associations between these constructs. Inferential analysis refers to the statistical testing of hypotheses (theory testing). In this chapter, we will examine statistical techniques used for descriptive analysis, and the next chapter will examine statistical techniques for inferential analysis. Much of today’s quantitative data analysis is conducted using software programs such as SPSS or SAS. Readers are advised to familiarise themselves with one of these programs for understanding the concepts described in this chapter.

Data preparation

In research projects, data may be collected from a variety of sources: postal surveys, interviews, pretest or posttest experimental data, observational data, and so forth. This data must be converted into a machine-readable, numeric format, such as in a spreadsheet or a text file, so that they can be analysed by computer programs like SPSS or SAS. Data preparation usually follows the following steps:

Data coding. Coding is the process of converting data into numeric format. A codebook should be created to guide the coding process. A codebook is a comprehensive document containing a detailed description of each variable in a research study, items or measures for that variable, the format of each item (numeric, text, etc.), the response scale for each item (i.e., whether it is measured on a nominal, ordinal, interval, or ratio scale, and whether this scale is a five-point, seven-point scale, etc.), and how to code each value into a numeric format. For instance, if we have a measurement item on a seven-point Likert scale with anchors ranging from ‘strongly disagree’ to ‘strongly agree’, we may code that item as 1 for strongly disagree, 4 for neutral, and 7 for strongly agree, with the intermediate anchors in between. Nominal data such as industry type can be coded in numeric form using a coding scheme such as: 1 for manufacturing, 2 for retailing, 3 for financial, 4 for healthcare, and so forth (of course, nominal data cannot be analysed statistically). Ratio scale data such as age, income, or test scores can be coded as entered by the respondent. Sometimes, data may need to be aggregated into a different form than the format used for data collection. For instance, if a survey measuring a construct such as ‘benefits of computers’ provided respondents with a checklist of benefits that they could select from, and respondents were encouraged to choose as many of those benefits as they wanted, then the total number of checked items could be used as an aggregate measure of benefits. Note that many other forms of data—such as interview transcripts—cannot be converted into a numeric format for statistical analysis. Codebooks are especially important for large complex studies involving many variables and measurement items, where the coding process is conducted by different people, to help the coding team code data in a consistent manner, and also to help others understand and interpret the coded data.

Data entry. Coded data can be entered into a spreadsheet, database, text file, or directly into a statistical program like SPSS. Most statistical programs provide a data editor for entering data. However, these programs store data in their own native format—e.g., SPSS stores data as .sav files—which makes it difficult to share that data with other statistical programs. Hence, it is often better to enter data into a spreadsheet or database where it can be reorganised as needed, shared across programs, and subsets of data can be extracted for analysis. Smaller data sets with less than 65,000 observations and 256 items can be stored in a spreadsheet created using a program such as Microsoft Excel, while larger datasets with millions of observations will require a database. Each observation can be entered as one row in the spreadsheet, and each measurement item can be represented as one column. Data should be checked for accuracy during and after entry via occasional spot checks on a set of items or observations. Furthermore, while entering data, the coder should watch out for obvious evidence of bad data, such as the respondent selecting the ‘strongly agree’ response to all items irrespective of content, including reverse-coded items. If so, such data can be entered but should be excluded from subsequent analysis.

Data transformation. Sometimes, it is necessary to transform data values before they can be meaningfully interpreted. For instance, reverse coded items—where items convey the opposite meaning of that of their underlying construct—should be reversed (e.g., in a 1-7 interval scale, 8 minus the observed value will reverse the value) before they can be compared or combined with items that are not reverse coded. Other kinds of transformations may include creating scale measures by adding individual scale items, creating a weighted index from a set of observed measures, and collapsing multiple values into fewer categories (e.g., collapsing incomes into income ranges).

Univariate analysis

Univariate analysis—or analysis of a single variable—refers to a set of statistical techniques that can describe the general properties of one variable. Univariate statistics include: frequency distribution, central tendency, and dispersion. The frequency distribution of a variable is a summary of the frequency—or percentages—of individual values or ranges of values for that variable. For instance, we can measure how many times a sample of respondents attend religious services—as a gauge of their ‘religiosity’—using a categorical scale: never, once per year, several times per year, about once a month, several times per month, several times per week, and an optional category for ‘did not answer’. If we count the number or percentage of observations within each category—except ‘did not answer’ which is really a missing value rather than a category—and display it in the form of a table, as shown in Figure 14.1, what we have is a frequency distribution. This distribution can also be depicted in the form of a bar chart, as shown on the right panel of Figure 14.1, with the horizontal axis representing each category of that variable and the vertical axis representing the frequency or percentage of observations within each category.

With very large samples, where observations are independent and random, the frequency distribution tends to follow a plot that looks like a bell-shaped curve—a smoothed bar chart of the frequency distribution—similar to that shown in Figure 14.2. Here most observations are clustered toward the centre of the range of values, with fewer and fewer observations clustered toward the extreme ends of the range. Such a curve is called a normal distribution .

Lastly, the mode is the most frequently occurring value in a distribution of values. In the previous example, the most frequently occurring value is 15, which is the mode of the above set of test scores. Note that any value that is estimated from a sample, such as mean, median, mode, or any of the later estimates are called a statistic .

Bivariate analysis

Bivariate analysis examines how two variables are related to one another. The most common bivariate statistic is the bivariate correlation —often, simply called ‘correlation’—which is a number between -1 and +1 denoting the strength of the relationship between two variables. Say that we wish to study how age is related to self-esteem in a sample of 20 respondents—i.e., as age increases, does self-esteem increase, decrease, or remain unchanged?. If self-esteem increases, then we have a positive correlation between the two variables, if self-esteem decreases, then we have a negative correlation, and if it remains the same, we have a zero correlation. To calculate the value of this correlation, consider the hypothetical dataset shown in Table 14.1.

After computing bivariate correlation, researchers are often interested in knowing whether the correlation is significant (i.e., a real one) or caused by mere chance. Answering such a question would require testing the following hypothesis:

Social Science Research: Principles, Methods and Practices (Revised edition) Copyright © 2019 by Anol Bhattacherjee is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalising your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organising data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles

Edward barroga.

1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.

INTRODUCTION

Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6

It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4

There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.

DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES

A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5

On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4

Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8

Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12

CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES

Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13

There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10

TYPES OF RESEARCH QUESTIONS AND HYPOTHESES

Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .

Research questions in quantitative research

In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .

Hypotheses in quantitative research

In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .

Research questions in qualitative research

Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15

There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .

Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15

Hypotheses in qualitative research

Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1

FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES

Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14

The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14

As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.

a These statements were composed for comparison and illustrative purposes only.

b These statements are direct quotes from Higashihara and Horiuchi. 16

a This statement is a direct quote from Shimoda et al. 17

The other statements were composed for comparison and illustrative purposes only.

CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES

To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .

Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.

Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12

In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.

EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES

• EXAMPLE 1. Descriptive research question (quantitative research)
• - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
• “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
• RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
• EXAMPLE 2. Relationship research question (quantitative research)
• - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
• “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
• Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
• EXAMPLE 3. Comparative research question (quantitative research)
• - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
• “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
• RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
• STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
• EXAMPLE 4. Exploratory research question (qualitative research)
• - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
• “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
• EXAMPLE 5. Relationship research question (quantitative research)
• - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
• “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23

EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES

• EXAMPLE 1. Working hypothesis (quantitative research)
• - A hypothesis that is initially accepted for further research to produce a feasible theory
• “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
• “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
• EXAMPLE 2. Exploratory hypothesis (qualitative research)
• - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
• “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
• “Conclusion
• Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
• EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
• “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
• Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
• EXAMPLE 4. Statistical hypothesis (quantitative research)
• - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
• “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
• “Statistical Analysis
• ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27

EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS

• EXAMPLE 1. Background, hypotheses, and aims are provided
• “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
• “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
• “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
• EXAMPLE 2. Background, hypotheses, and aims are provided
• “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
• “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
• EXAMPLE 3. Background, aim, and hypothesis are provided
• “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
• “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
• “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30

Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Barroga E, Matanguihan GJ.
• Methodology: Barroga E, Matanguihan GJ.
• Writing - original draft: Barroga E, Matanguihan GJ.
• Writing - review & editing: Barroga E, Matanguihan GJ.

Table of Contents

Types of statistical analysis, importance of statistical analysis, benefits of statistical analysis, statistical analysis process, statistical analysis methods, statistical analysis software, statistical analysis examples, career in statistical analysis, choose the right program, become proficient in statistics today, what is statistical analysis types, methods and examples.

Statistical analysis is the process of collecting and analyzing data in order to discern patterns and trends. It is a method for removing bias from evaluating data by employing numerical analysis. This technique is useful for collecting the interpretations of research, developing statistical models, and planning surveys and studies.

Statistical analysis is a scientific tool in AI and ML that helps collect and analyze large amounts of data to identify common patterns and trends to convert them into meaningful information. In simple words, statistical analysis is a data analysis tool that helps draw meaningful conclusions from raw and unstructured data. 

The conclusions are drawn using statistical analysis facilitating decision-making and helping businesses make future predictions on the basis of past trends. It can be defined as a science of collecting and analyzing data to identify trends and patterns and presenting them. Statistical analysis involves working with numbers and is used by businesses and other institutions to make use of data to derive meaningful information. 

Given below are the 6 types of statistical analysis:

Descriptive Analysis

Descriptive statistical analysis involves collecting, interpreting, analyzing, and summarizing data to present them in the form of charts, graphs, and tables. Rather than drawing conclusions, it simply makes the complex data easy to read and understand.

Inferential Analysis

The inferential statistical analysis focuses on drawing meaningful conclusions on the basis of the data analyzed. It studies the relationship between different variables or makes predictions for the whole population.

Predictive Analysis

Predictive statistical analysis is a type of statistical analysis that analyzes data to derive past trends and predict future events on the basis of them. It uses machine learning algorithms, data mining , data modelling , and artificial intelligence to conduct the statistical analysis of data.

Prescriptive Analysis

The prescriptive analysis conducts the analysis of data and prescribes the best course of action based on the results. It is a type of statistical analysis that helps you make an informed decision. 

Exploratory Data Analysis

Exploratory analysis is similar to inferential analysis, but the difference is that it involves exploring the unknown data associations. It analyzes the potential relationships within the data. 

Causal Analysis

The causal statistical analysis focuses on determining the cause and effect relationship between different variables within the raw data. In simple words, it determines why something happens and its effect on other variables. This methodology can be used by businesses to determine the reason for failure. 

Statistical analysis eliminates unnecessary information and catalogs important data in an uncomplicated manner, making the monumental work of organizing inputs appear so serene. Once the data has been collected, statistical analysis may be utilized for a variety of purposes. Some of them are listed below:

• The statistical analysis aids in summarizing enormous amounts of data into clearly digestible chunks.
• The statistical analysis aids in the effective design of laboratory, field, and survey investigations.
• Statistical analysis may help with solid and efficient planning in any subject of study.
• Statistical analysis aid in establishing broad generalizations and forecasting how much of something will occur under particular conditions.
• Statistical methods, which are effective tools for interpreting numerical data, are applied in practically every field of study. Statistical approaches have been created and are increasingly applied in physical and biological sciences, such as genetics.
• Statistical approaches are used in the job of a businessman, a manufacturer, and a researcher. Statistics departments can be found in banks, insurance businesses, and government agencies.
• A modern administrator, whether in the public or commercial sector, relies on statistical data to make correct decisions.
• Politicians can utilize statistics to support and validate their claims while also explaining the issues they address.

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Statistical analysis can be called a boon to mankind and has many benefits for both individuals and organizations. Given below are some of the reasons why you should consider investing in statistical analysis:

• It can help you determine the monthly, quarterly, yearly figures of sales profits, and costs making it easier to make your decisions.
• It can help you make informed and correct decisions.
• It can help you identify the problem or cause of the failure and make corrections. For example, it can identify the reason for an increase in total costs and help you cut the wasteful expenses.
• It can help you conduct market analysis and make an effective marketing and sales strategy.
• It helps improve the efficiency of different processes.

Given below are the 5 steps to conduct a statistical analysis that you should follow:

• Step 1: Identify and describe the nature of the data that you are supposed to analyze.
• Step 2: The next step is to establish a relation between the data analyzed and the sample population to which the data belongs. 
• Step 3: The third step is to create a model that clearly presents and summarizes the relationship between the population and the data.
• Step 4: Prove if the model is valid or not.
• Step 5: Use predictive analysis to predict future trends and events likely to happen. 

Although there are various methods used to perform data analysis, given below are the 5 most used and popular methods of statistical analysis:

Mean or average mean is one of the most popular methods of statistical analysis. Mean determines the overall trend of the data and is very simple to calculate. Mean is calculated by summing the numbers in the data set together and then dividing it by the number of data points. Despite the ease of calculation and its benefits, it is not advisable to resort to mean as the only statistical indicator as it can result in inaccurate decision making. 

Standard Deviation

Standard deviation is another very widely used statistical tool or method. It analyzes the deviation of different data points from the mean of the entire data set. It determines how data of the data set is spread around the mean. You can use it to decide whether the research outcomes can be generalized or not. 

Regression is a statistical tool that helps determine the cause and effect relationship between the variables. It determines the relationship between a dependent and an independent variable. It is generally used to predict future trends and events.

Hypothesis Testing

Hypothesis testing can be used to test the validity or trueness of a conclusion or argument against a data set. The hypothesis is an assumption made at the beginning of the research and can hold or be false based on the analysis results. 

Sample Size Determination

Sample size determination or data sampling is a technique used to derive a sample from the entire population, which is representative of the population. This method is used when the size of the population is very large. You can choose from among the various data sampling techniques such as snowball sampling, convenience sampling, and random sampling. 

Everyone can't perform very complex statistical calculations with accuracy making statistical analysis a time-consuming and costly process. Statistical software has become a very important tool for companies to perform their data analysis. The software uses Artificial Intelligence and Machine Learning to perform complex calculations, identify trends and patterns, and create charts, graphs, and tables accurately within minutes. 

Look at the standard deviation sample calculation given below to understand more about statistical analysis.

The weights of 5 pizza bases in cms are as follows:

Calculation of Mean = (9+2+5+4+12)/5 = 32/5 = 6.4

Calculation of mean of squared mean deviation = (6.76+19.36+1.96+5.76+31.36)/5 = 13.04

Sample Variance = 13.04

Standard deviation = √13.04 = 3.611

A Statistical Analyst's career path is determined by the industry in which they work. Anyone interested in becoming a Data Analyst may usually enter the profession and qualify for entry-level Data Analyst positions right out of high school or a certificate program — potentially with a Bachelor's degree in statistics, computer science, or mathematics. Some people go into data analysis from a similar sector such as business, economics, or even the social sciences, usually by updating their skills mid-career with a statistical analytics course.

Statistical Analyst is also a great way to get started in the normally more complex area of data science. A Data Scientist is generally a more senior role than a Data Analyst since it is more strategic in nature and necessitates a more highly developed set of technical abilities, such as knowledge of multiple statistical tools, programming languages, and predictive analytics models.

Aspiring Data Scientists and Statistical Analysts generally begin their careers by learning a programming language such as R or SQL. Following that, they must learn how to create databases, do basic analysis, and make visuals using applications such as Tableau. However, not every Statistical Analyst will need to know how to do all of these things, but if you want to advance in your profession, you should be able to do them all.

Based on your industry and the sort of work you do, you may opt to study Python or R, become an expert at data cleaning, or focus on developing complicated statistical models.

You could also learn a little bit of everything, which might help you take on a leadership role and advance to the position of Senior Data Analyst. A Senior Statistical Analyst with vast and deep knowledge might take on a leadership role leading a team of other Statistical Analysts. Statistical Analysts with extra skill training may be able to advance to Data Scientists or other more senior data analytics positions.

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Hope this article assisted you in understanding the importance of statistical analysis in every sphere of life. Artificial Intelligence (AI) can help you perform statistical analysis and data analysis very effectively and efficiently. 

If you are a science wizard and fascinated by the role of AI in statistical analysis, check out this amazing Caltech Post Graduate Program in AI & ML course in collaboration with Caltech. With a comprehensive syllabus and real-life projects, this course is one of the most popular courses and will help you with all that you need to know about Artificial Intelligence. 

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Statistical Monitoring and Analysis Lead (Associate Director, Quantitative Science)

• Proficiency in statistics, advanced data science methods and application, and programming.
• Experience in developing fit-for-purpose statistical methodologies and tools.
• Excellent communication and collaboration.
• Excellent matrix team leadership and interpersonal skills.
• Subject matter expertise in applying statistics and problem solving in related areas, such as RBM, statistical monitoring, research experiments, and AI/ML.
• Scientific curiosity
• Leading a Data Science project team and collaborating with the study team.
• Directing and supporting all data science activities that contribute to the statistical monitoring of clinical trials.
• Leading the statistical monitoring of clinical trials for RBM studies.
• Functioning as a statistical and analytical subject matter expert in statistical issues
• Ensuring the development and operationalization of fit-for-purpose and effective statistical methodologies in the monitoring of clinical trials, including continuous development of analysis modules, libraries, and data visualization/reporting.
• Ensuring the execution of RBM processes related to CSM and Quality Tolerance Limits (QTLs) throughout the study and working with the RBM business process owner to update processes as needed.
• Taking responsibility for study specific RBM components at study start-up, such as CSM/QTL and assisting with key deliverables such as Risk Assessment and Categorization Tool (RACT), critical data, and Key Risk Indicators (KRIs).
• Ensuring timely execution of CSM analysis and effective communication of discoveries to support Data Working Group (DWG)/Study Execution Team (SET) monitoring decisions.
• Collaborating effectively with internal stakeholders from Clinical Development, Global Study Operation, Statistical Science, Data Management Science, as well as external stakeholders (e.g., RBM system vendor, CRO, etc.).
• Collaborating with Data Management Science to provide statistical consultation for other data validation activities outside of CSM and QTL.
• Proactively and efficiently working with study team to organize, plan, manage, and control deliverables against goals and timelines.
• Keeping abreast of new RBM methodologies and regulatory guidance.
• Provide statistical support for experimental design, analysis, interpretation, and reporting of studies in research, biomarker development, manufacturing, and other areas.
• Develop statistical algorithms and specifications for applications that enable researchers to analyze repetitive experiments.
• Explore and develop the use of AI and ML for business impact and problem solving.
• Proven ability to effectively collaborate with cross-functional teams.
• Familiarity with clinical trial data and processes.
• Knowledge of risk-based monitoring of clinical trials and statistical methodology; hands-on experience in statistical monitoring preferred.
• Proficiency in developing and operationalizing fit-for-purpose analyses to assess study-specific risks in clinical trials.
• Adaptability and ability to thrive in a constantly changing, diverse, and matrixed environment.
• Advanced expertise in theoretical and applied statistics or other relevant data sciences.
• Extensive knowledge of statistical analysis methods, with a focus on statistical monitoring.
• Strong programming skills in SAS, R, Python, and other statistical software packages.
• Proficiency in developing specifications and designing analysis modules to operationalize CSM analysis, visualization, and reporting.
• Demonstrated ability to lead, motivate, and mentor both internal and contract staff.
• Effective review and evaluation skills for documents drafted by staff.
• Thorough understanding of regulatory regulations and guidelines, particularly in the context of RBM.

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