step hypothesis procedure

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Biology library

Course: biology library   >   unit 1, the scientific method.

• Controlled experiments
• The scientific method and experimental design

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation..

• Observation: the toaster won't toast.

2. Ask a question.

• Question: Why won't my toaster toast?

3. Propose a hypothesis.

• Hypothesis: Maybe the outlet is broken.

4. Make predictions.

• Prediction: If I plug the toaster into a different outlet, then it will toast the bread.

5. Test the predictions.

• Test of prediction: Plug the toaster into a different outlet and try again.
• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• Iteration time!
• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

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Hypothesis Testing Framework

Now that we've seen an example and explored some of the themes for hypothesis testing, let's specify the procedure that we will follow.

Hypothesis Testing Steps

The formal framework and steps for hypothesis testing are as follows:

• Identify and define the parameter of interest
• Define the competing hypotheses to test
• Set the evidence threshold, formally called the significance level
• Generate or use theory to specify the sampling distribution and check conditions
• Calculate the test statistic and p-value
• Evaluate your results and write a conclusion in the context of the problem.

We'll discuss each of these steps below.

Identify Parameter of Interest

First, I like to specify and define the parameter of interest. What is the population that we are interested in? What characteristic are we measuring?

By defining our population of interest, we can confirm that we are truly using sample data. If we find that we actually have population data, our inference procedures are not needed. We could proceed by summarizing our population data.

By identifying and defining the parameter of interest, we can confirm that we use appropriate methods to summarize our variable of interest. We can also focus on the specific process needed for our parameter of interest.

In our example from the last page, the parameter of interest would be the population mean time that a host has been on Airbnb for the population of all Chicago listings on Airbnb in March 2023. We could represent this parameter with the symbol $\mu$. It is best practice to fully define $\mu$ both with words and symbol.

Define the Hypotheses

For hypothesis testing, we need to decide between two competing theories. These theories must be statements about the parameter. Although we won't have the population data to definitively select the correct theory, we will use our sample data to determine how reasonable our "skeptic's theory" is.

The first hypothesis is called the null hypothesis, $H_0$. This can be thought of as the "status quo", the "skeptic's theory", or that nothing is happening.

Examples of null hypotheses include that the population proportion is equal to 0.5 ($p = 0.5$), the population median is equal to 12 ($M = 12$), or the population mean is equal to 14.5 ($\mu = 14.5$).

The second hypothesis is called the alternative hypothesis, $H_a$ or $H_1$. This can be thought of as the "researcher's hypothesis" or that something is happening. This is what we'd like to convince the skeptic to believe. In most cases, the desired outcome of the researcher is to conclude that the alternative hypothesis is reasonable to use moving forward.

Examples of alternative hypotheses include that the population proportion is greater than 0.5 ($p > 0.5$), the population median is less than 12 ($M < 12$), or the population mean is not equal to 14.5 ($\mu \neq 14.5$).

There are a few requirements for the hypotheses:

• the hypotheses must be about the same population parameter,
• the hypotheses must have the same null value (provided number to compare to),
• the null hypothesis must have the equality (the equals sign must be in the null hypothesis),
• the alternative hypothesis must not have the equality (the equals sign cannot be in the alternative hypothesis),
• there must be no overlap between the null and alternative hypothesis.

You may have previously seen null hypotheses that include more than an equality (e.g. $p \le 0.5$). As long as there is an equality in the null hypothesis, this is allowed. For our purposes, we will simplify this statement to ($p = 0.5$).

To summarize from above, possible hypotheses statements are:

$H_0: p = 0.5$ vs. $H_a: p > 0.5$

$H_0: M = 12$ vs. $H_a: M < 12$

$H_0: \mu = 14.5$ vs. $H_a: \mu \neq 14.5$

In our second example about Airbnb hosts, our hypotheses would be:

$H_0: \mu = 2100$ vs. $H_a: \mu > 2100$.

Set Threshold (Significance Level)

There is one more step to complete before looking at the data. This is to set the threshold needed to convince the skeptic. This threshold is defined as an $\alpha$ significance level. We'll define exactly what the $\alpha$ significance level means later. For now, smaller $\alpha$s correspond to more evidence being required to convince the skeptic.

A few common $\alpha$ levels include 0.1, 0.05, and 0.01.

For our Airbnb hosts example, we'll set the threshold as 0.02.

Determine the Sampling Distribution of the Sample Statistic

The first step (as outlined above) is the identify the parameter of interest. What is the best estimate of the parameter of interest? Typically, it will be the sample statistic that corresponds to the parameter. This sample statistic, along with other features of the distribution will prove especially helpful as we continue the hypothesis testing procedure.

However, we do have a decision at this step. We can choose to use simulations with a resampling approach or we can choose to rely on theory if we are using proportions or means. We then also need to confirm that our results and conclusions will be valid based on the available data.

Required Condition

The one required assumption, regardless of approach (resampling or theory), is that the sample is random and representative of the population of interest. In other words, we need our sample to be a reasonable sample of data from the population.

Using Simulations and Resampling

If we'd like to use a resampling approach, we have no (or minimal) additional assumptions to check. This is because we are relying on the available data instead of assumptions.

We do need to adjust our data to be consistent with the null hypothesis (or skeptic's claim). We can then rely on our resampling approach to estimate a plausible sampling distribution for our sample statistic.

Recall that we took this approach on the last page. Before simulating our estimated sampling distribution, we adjusted the mean of the data so that it matched with our skeptic's claim, shown in the code below.

We'll see a few more examples on the next page.

Using Theory

On the other hand, we could rely on theory in order to estimate the sampling distribution of our desired statistic. Recall that we had a few different options to rely on:

• the CLT for the sampling distribution of a sample mean
• the binomial distribution for the sampling distribution of a proportion (or count)
• the Normal approximation of a binomial distribution (using the CLT) for the sampling distribution of a proportion

If relying on the CLT to specify the underlying sampling distribution, you also need to confirm:

• having a random sample and
• having a sample size that is less than 10% of the population size if the sampling is done without replacement
• having a Normally distributed population for a quantitative variable OR
• having a large enough sample size (usually at least 25) for a quantitative variable
• having a large enough sample size for a categorical variable (defined by $np$ and $n(1-p)$ being at least 10)

If relying on the binomial distribution to specify the underlying sampling distribution, you need to confirm:

• having a set number of trials, $n$
• having the same probability of success, $p$ for each observation

After determining the appropriate theory to use, we should check our conditions and then specify the sampling distribution for our statistic.

For the Airbnb hosts example, we have what we've assumed to be a random sample. It is not taken with replacement, so we also need to assume that our sample size (700) is less than 10% of our population size. In other words, we need to assume that the population of Chicago Airbnbs in March 2023 was at least 7000. Since we do have our (presumed) population data available, we can confirm that there were at least 7000 Chicago Airbnbs in the population in 2023.

Additionally, we can confirm that normality of the sampling distribution applies for the CLT to apply. Our sample size is more than 25 and the parameter of interest is a mean, so this meets our necessary criteria for the normality condition to be valid.

With the conditions now met, we can estimate our sampling distribution. From the CLT, we know that the distribution for the sample mean should be $\bar{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$.

Now, we face our next challenge -- what to plug in as the mean and standard error for this distribution. Since we are adopting the skeptic's point of view for the purpose of this approach, we can plug in the value of $\mu_0 = 2100$. We also know that the sample size $n$ is 700. But what should we plug in for the population standard deviation $\sigma$?

When we don't know the value of a parameter, we will generally plug in our best estimate for the parameter. In this case, that corresponds to plugging in $\hat{\sigma}$, or our sample standard deviation.

Now, our estimated sampling distribution based on the CLT is: $\bar{X} \sim N(2100, 41.4045)$.

If we compare to our corresponding skeptic's sampling distribution on the last page, we can confirm that the theoretical sampling distribution is similar to the simulated sampling distribution based on resampling.

Assumptions not met

What do we do if the necessary conditions aren't met for the sampling distribution? Because the simulation-based resampling approach has minimal assumptions, we should be able to use this approach to produce valid results as long as the provided data is representative of the population.

The theory-based approach has more conditions, and we may not be able to meet all of the necessary conditions. For example, if our parameter is something other than a mean or proportion, we may not have appropriate theory. Additionally, we may not have a large enough sample size.

• First, we could consider changing approaches to the simulation-based one.
• Second, we might look at how we could meet the necessary conditions better. In some cases, we may be able to redefine groups or make adjustments so that the setup of the test is closer to what is needed.
• As a last resort, we may be able to continue following the hypothesis testing steps. In this case, your calculations may not be valid or exact; however, you might be able to use them as an estimate or an approximation. It would be crucial to specify the violation and approximation in any conclusions or discussion of the test.

Calculate the evidence with statistics and p-values

Now, it's time to calculate how much evidence the sample contains to convince the skeptic to change their mind. As we saw above, we can convince the skeptic to change their mind by demonstrating that our sample is unlikely to occur if their theory is correct.

How do we do this? We do this by calculating a probability associated with our observed value for the statistic.

For example, for our situation, we want to convince the skeptic that the population mean is actually greater than 2100 days. We do that by calculating the probability that a sample mean would be as large or larger than what we observed in our actual sample, which was 2188 days. Why do we need the larger portion? We use the larger portion because a sample mean of 2200 days also provides evidence that the population mean is larger than 2100 days; it isn't limited to exactly what we observed in our sample. We call this specific probability the p-value.

That is, the p-value is the probability of observing a test statistic as extreme or more extreme (as determined by the alternative hypothesis), assuming the null hypothesis is true.

Our observed p-value for the Airbnb host example demonstrates that the probability of getting a sample mean host time of 2188 days (the value from our sample) or more is 1.46%, assuming that the true population mean is 2100 days.

Test statistic

Notice that the formal definition of a p-value mentions a test statistic . In most cases, this word can be replaced with "statistic" or "sample" for an equivalent statement.

Oftentimes, we'll see that our sample statistic can be used directly as the test statistic, as it was above. We could equivalently adjust our statistic to calculate a test statistic. This test statistic is often calculated as:

$\text{test statistic} = \frac{\text{estimate} - \text{hypothesized value}}{\text{standard error of estimate}}$

P-value Calculation Options

Note also that the p-value definition includes a probability associated with a test statistic being as extreme or more extreme (as determined by the alternative hypothesis . How do we determine the area that we consider when calculating the probability. This decision is determined by the inequality in the alternative hypothesis.

For example, when we were trying to convince the skeptic that the population mean is greater than 2100 days, we only considered those sample means that we at least as large as what we observed -- 2188 days or more.

If instead we were trying to convince the skeptic that the population mean is less than 2100 days ($H_a: \mu < 2100$), we would consider all sample means that were at most what we observed - 2188 days or less. In this case, our p-value would be quite large; it would be around 99.5%. This large p-value demonstrates that our sample does not support the alternative hypothesis. In fact, our sample would encourage us to choose the null hypothesis instead of the alternative hypothesis of $\mu < 2100$, as our sample directly contradicts the statement in the alternative hypothesis.

If we wanted to convince the skeptic that they were wrong and that the population mean is anything other than 2100 days ($H_a: \mu \neq 2100$), then we would want to calculate the probability that a sample mean is at least 88 days away from 2100 days. That is, we would calculate the probability corresponding to 2188 days or more or 2012 days or less. In this case, our p-value would be roughly twice the previously calculated p-value.

We could calculate all of those probabilities using our sampling distributions, either simulated or theoretical, that we generated in the previous step. If we chose to calculate a test statistic as defined in the previous section, we could also rely on standard normal distributions to calculate our p-value.

Evaluate your results and write conclusion in context of problem

Once you've gathered your evidence, it's now time to make your final conclusions and determine how you might proceed.

In traditional hypothesis testing, you often make a decision. Recall that you have your threshold (significance level $\alpha$) and your level of evidence (p-value). We can compare the two to determine if your p-value is less than or equal to your threshold. If it is, you have enough evidence to persuade your skeptic to change their mind. If it is larger than the threshold, you don't have quite enough evidence to convince the skeptic.

Common formal conclusions (if given in context) would be:

• I have enough evidence to reject the null hypothesis (the skeptic's claim), and I have sufficient evidence to suggest that the alternative hypothesis is instead true.
• I do not have enough evidence to reject the null hypothesis (the skeptic's claim), and so I do not have sufficient evidence to suggest the alternative hypothesis is true.

The only decision that we can make is to either reject or fail to reject the null hypothesis (we cannot "accept" the null hypothesis). Because we aren't actively evaluating the alternative hypothesis, we don't want to make definitive decisions based on that hypothesis. However, when it comes to making our conclusion for what to use going forward, we frame this on whether we could successfully convince someone of the alternative hypothesis.

A less formal conclusion might look something like:

Based on our sample of Chicago Airbnb listings, it seems as if the mean time since a host has been on Airbnb (for all Chicago Airbnb listings) is more than 5.75 years.

Significance Level Interpretation

We've now seen how the significance level $\alpha$ is used as a threshold for hypothesis testing. What exactly is the significance level?

The significance level $\alpha$ has two primary definitions. One is that the significance level is the maximum probability required to reject the null hypothesis; this is based on how the significance level functions within the hypothesis testing framework. The second definition is that this is the probability of rejecting the null hypothesis when the null hypothesis is true; in other words, this is the probability of making a specific type of error called a Type I error.

Why do we have to be comfortable making a Type I error? There is always a chance that the skeptic was originally correct and we obtained a very unusual sample. We don't want to the skeptic to be so convinced of their theory that no evidence can convince them. In this case, we need the skeptic to be convinced as long as the evidence is strong enough . Typically, the probability threshold will be low, to reduce the number of errors made. This also means that a decent amount of evidence will be needed to convince the skeptic to abandon their position in favor of the alternative theory.

p-value Limitations and Misconceptions

In comparison to the $\alpha$ significance level, we also need to calculate the evidence against the null hypothesis with the p-value.

The p-value is the probability of getting a test statistic as extreme or more extreme (in the direction of the alternative hypothesis), assuming the null hypothesis is true.

Recently, p-values have gotten some bad press in terms of how they are used. However, that doesn't mean that p-values should be abandoned, as they still provide some helpful information. Below, we'll describe what p-values don't mean, and how they should or shouldn't be used to make decisions.

Factors that affect a p-value

What features affect the size of a p-value?

• the null value, or the value assumed under the null hypothesis
• the effect size (the difference between the null value under the null hypothesis and the true value of the parameter)
• the sample size

More evidence against the null hypothesis will be obtained if the effect size is larger and if the sample size is larger.

Misconceptions

We gave a definition for p-values above. What are some examples that p-values don't mean?

• A p-value is not the probability that the null hypothesis is correct
• A p-value is not the probability that the null hypothesis is incorrect
• A p-value is not the probability of getting your specific sample
• A p-value is not the probability that the alternative hypothesis is correct
• A p-value is not the probability that the alternative hypothesis is incorrect
• A p-value does not indicate the size of the effect

Our p-value is a way of measuring the evidence that your sample provides against the null hypothesis, assuming the null hypothesis is in fact correct.

Using the p-value to make a decision

Why is there bad press for a p-value? You may have heard about the standard $\alpha$ level of 0.05. That is, we would be comfortable with rejecting the null hypothesis once in 20 attempts when the null hypothesis is really true. Recall that we reject the null hypothesis when the p-value is less than or equal to the significance level.

Consider what would happen if you have two different p-values: 0.049 and 0.051.

In essence, these two p-values represent two very similar probabilities (4.9% vs. 5.1%) and very similar levels of evidence against the null hypothesis. However, when we make our decision based on our threshold, we would make two different decisions (reject and fail to reject, respectively). Should this decision really be so simplistic? I would argue that the difference shouldn't be so severe when the sample statistics are likely very similar. For this reason, I (and many other experts) strongly recommend using the p-value as a measure of evidence and including it with your conclusion.

Putting too much emphasis on the decision (and having a significant result) has created a culture of misusing p-values. For this reason, understanding your p-value itself is crucial.

Searching for p-values

The other concern with setting a definitive threshold of 0.05 is that some researchers will begin performing multiple tests until finding a p-value that is small enough. However, with a p-value of 0.05, we know that we will have a p-value less than 0.05 1 time out of every 20 times, even when the null hypothesis is true.

This means that if researchers start hunting for p-values that are small (sometimes called p-hacking), then they are likely to identify a small p-value every once in a while by chance alone. Researchers might then publish that result, even though the result is actually not informative. For this reason, it is recommended that researchers write a definitive analysis plan to prevent performing multiple tests in search of a result that occurs by chance alone.

Best Practices

With all of this in mind, what should we do when we have our p-value? How can we prevent or reduce misuse of a p-value?

• Report the p-value along with the conclusion
• Specify the effect size (the value of the statistic)
• Define an analysis plan before looking at the data
• Interpret the p-value clearly to specify what it indicates
• Consider using an alternate statistical approach, the confidence interval, discussed next, when appropriate

Statistics Made Easy

Introduction to Hypothesis Testing

A statistical hypothesis is an assumption about a population parameter .

For example, we may assume that the mean height of a male in the U.S. is 70 inches.

The assumption about the height is the statistical hypothesis and the true mean height of a male in the U.S. is the population parameter .

A hypothesis test is a formal statistical test we use to reject or fail to reject a statistical hypothesis.

The Two Types of Statistical Hypotheses

To test whether a statistical hypothesis about a population parameter is true, we obtain a random sample from the population and perform a hypothesis test on the sample data.

There are two types of statistical hypotheses:

The null hypothesis , denoted as H 0 , is the hypothesis that the sample data occurs purely from chance.

The alternative hypothesis , denoted as H 1 or H a , is the hypothesis that the sample data is influenced by some non-random cause.

Hypothesis Tests

A hypothesis test consists of five steps:

1. State the hypotheses. 

State the null and alternative hypotheses. These two hypotheses need to be mutually exclusive, so if one is true then the other must be false.

2. Determine a significance level to use for the hypothesis.

Decide on a significance level. Common choices are .01, .05, and .1. 

3. Find the test statistic.

Find the test statistic and the corresponding p-value. Often we are analyzing a population mean or proportion and the general formula to find the test statistic is: (sample statistic – population parameter) / (standard deviation of statistic)

4. Reject or fail to reject the null hypothesis.

Using the test statistic or the p-value, determine if you can reject or fail to reject the null hypothesis based on the significance level.

The p-value  tells us the strength of evidence in support of a null hypothesis. If the p-value is less than the significance level, we reject the null hypothesis.

5. Interpret the results. 

Interpret the results of the hypothesis test in the context of the question being asked. 

The Two Types of Decision Errors

There are two types of decision errors that one can make when doing a hypothesis test:

Type I error: You reject the null hypothesis when it is actually true. The probability of committing a Type I error is equal to the significance level, often called  alpha , and denoted as α.

Type II error: You fail to reject the null hypothesis when it is actually false. The probability of committing a Type II error is called the Power of the test or  Beta , denoted as β.

One-Tailed and Two-Tailed Tests

A statistical hypothesis can be one-tailed or two-tailed.

A one-tailed hypothesis involves making a “greater than” or “less than ” statement.

For example, suppose we assume the mean height of a male in the U.S. is greater than or equal to 70 inches. The null hypothesis would be H0: µ ≥ 70 inches and the alternative hypothesis would be Ha: µ < 70 inches.

A two-tailed hypothesis involves making an “equal to” or “not equal to” statement.

For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches. The null hypothesis would be H0: µ = 70 inches and the alternative hypothesis would be Ha: µ ≠ 70 inches.

Note: The “equal” sign is always included in the null hypothesis, whether it is =, ≥, or ≤.

Related:   What is a Directional Hypothesis?

Types of Hypothesis Tests

There are many different types of hypothesis tests you can perform depending on the type of data you’re working with and the goal of your analysis.

The following tutorials provide an explanation of the most common types of hypothesis tests:

Introduction to the One Sample t-test Introduction to the Two Sample t-test Introduction to the Paired Samples t-test Introduction to the One Proportion Z-Test Introduction to the Two Proportion Z-Test

Hey there. My name is Zach Bobbitt. I have a Master of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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6 Steps to Evaluate the Effectiveness of Statistical Hypothesis Testing

You know what is tragic? Having the potential to complete the research study but not doing the correct hypothesis testing. Quite often, researchers think the most challenging aspect of research is standardization of experiments, data analysis or writing the thesis! But in all honesty, creating an effective research hypothesis is the most crucial step in designing and executing a research study. An effective research hypothesis will provide researchers the correct basic structure for building the research question and objectives.

In this article, we will discuss how to formulate and identify an effective research hypothesis testing to benefit researchers in designing their research work.

Table of Contents

What Is Research Hypothesis Testing?

Hypothesis testing is a systematic procedure derived from the research question and decides if the results of a research study support a certain theory which can be applicable to the population. Moreover, it is a statistical test used to determine whether the hypothesis assumed by the sample data stands true to the entire population.

The purpose of testing the hypothesis is to make an inference about the population of interest on the basis of random sample taken from that population. Furthermore, it is the assumption which is tested to determine the relationship between two data sets.

Types of Statistical Hypothesis Testing

Source: https://www.youtube.com/c/365DataScience

1. there are two types of hypothesis in statistics, a. null hypothesis.

This is the assumption that the event will not occur or there is no relation between the compared variables. A null hypothesis has no relation with the study’s outcome unless it is rejected. Null hypothesis uses H0 as its symbol.

b. Alternate Hypothesis

The alternate hypothesis is the logical opposite of the null hypothesis. Furthermore, the acceptance of the alternative hypothesis follows the rejection of the null hypothesis. It uses H1 or Ha as its symbol

Hypothesis Testing Example: A sanitizer manufacturer company claims that its product kills 98% of germs on average. To put this company’s claim to test, create null and alternate hypothesis H0 (Null Hypothesis): Average = 98% H1/Ha (Alternate Hypothesis): The average is less than 98%

2. Depending on the population distribution, you can categorize the statistical hypothesis into two types.

A. simple hypothesis.

A simple hypothesis specifies an exact value for the parameter.

b. Composite Hypothesis

A composite hypothesis specifies a range of values.

Hypothesis Testing Example: A company claims to have achieved 1000 units as their average sales for this quarter. (Simple Hypothesis) The company claims to achieve the sales in the range of 900 to 100o units. (Composite Hypothesis).

3. Based on the type of statistical testing, the hypothesis in statistics is of two types.

A. one-tailed.

One-Tailed test or directional test considers a critical region of data which would result in rejection of the null hypothesis if the test sample falls in that data region. Therefore, accepting the alternate hypothesis. Furthermore, the critical distribution area in this test is one-sided which means the test sample is either greater or lesser than a specific value.

b. Two-Tailed

Two-Tailed test or nondirectional test is designed to show if the sample mean is significantly greater than and significantly less than the mean population. Here, the critical distribution area is two-sided. If the sample falls within the range, the alternate hypothesis is accepted and the null hypothesis is rejected.

Statistical Hypothesis Testing Example: Suppose H0: mean = 100 and H1: mean is not equal to 100 According to the H1, the mean can be greater than or less than 100. (Two-Tailed test) Similarly, if H0: mean >= 100, then H1: mean < 100 Here the mean is less than 100. (One-Tailed test)

Steps in Statistical Hypothesis Testing

Step 1: develop initial research hypothesis.

Research hypothesis is developed from research question. It is the prediction that you want to investigate. Moreover, an initial research hypothesis is important for restating the null and alternate hypothesis, to test the research question mathematically.

Step 2: State the null and alternate hypothesis based on your research hypothesis

Usually, the alternate hypothesis is your initial hypothesis that predicts relationship between variables. However, the null hypothesis is a prediction of no relationship between the variables you are interested in.

Step 3: Perform sampling and collection of data for statistical testing

It is important to perform sampling and collect data in way that assists the formulated research hypothesis. You will have to perform a statistical testing to validate your data and make statistical inferences about the population of your interest.

Step 4: Perform statistical testing based on the type of data you collected

There are various statistical tests available. Based on the comparison of within group variance and between group variance, you can carry out the statistical tests for the research study. If the between group variance is large enough and there is little or no overlap between groups, then the statistical test will show low p-value. (Difference between the groups is not a chance event).

Alternatively, if the within group variance is high compared to between group variance, then the statistical test shows a high p-value. (Difference between the groups is a chance event).

Step 5: Based on the statistical outcome, reject or fail to reject your null hypothesis

In most cases, you will use p-value generated from your statistical test to guide your decision. You will consider a predetermined level of significance of 0.05 for rejecting your null hypothesis , i.e. there is less than 5% chance of getting the results wherein the null hypothesis is true.

Step 6: Present your final results of hypothesis testing

You will present the results of your hypothesis in the results and discussion section of the research paper . In results section, you provide a brief summary of the data and a summary of the results of your statistical test. Meanwhile, in discussion, you can mention whether your results support your initial hypothesis.

Note that we never reject or fail to reject the alternate hypothesis. This is because the testing of hypothesis is not designed to prove or disprove anything. However, it is designed to test if a result is spuriously occurred, or by chance. Thus, statistical hypothesis testing becomes a crucial statistical tool to mathematically define the outcome of a research question.

Have you ever used hypothesis testing as a means of statistically analyzing your research data? How was your experience? Do write to us or comment below.

Well written and informative article.

good article

Nicely explained!

Its amazing & really helpful.

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12.3: Steps in Hypothesis Testing

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CHAPTER OBJECTIVES

By the end of this chapter, the student should be able to:

• Differentiate between Type I and Type II Errors
• Describe hypothesis testing in general and in practice
• Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
• Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.
• Conduct and interpret hypothesis tests for a single population proportion

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

A statistician will make a decision about these claims. This process is called "hypothesis testing." A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analysis of the data, to reject the null hypothesis. In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:

• Set up two contradictory hypotheses.
• Collect sample data (in homework problems, the data or summary statistics will be given to you).
• Determine the correct distribution to perform the hypothesis test.
• Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.
• Make a decision and write a meaningful conclusion.

To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See Appendix E .

• The desired confidence level.
• Information that is known about the distribution (for example, known standard deviation).
• The sample and its size.

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Hypothesis Testing w/ 21 Step-by-Step Examples!

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In statistical testing, also referred to as hypothesis testing, our goal is to show the credibility of a claim regarding the population.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

What Is Hypothesis Testing

Now it would be unreasonable to assume that we can test the entire population to determine the feasibility of every claim one might have.

Thus, we need a way to conclude an assumption is true or false by taking an appropriate sample and calculating a relevant statistic.

And knowing that we must expect that there will be some variation between the sample statistic that is calculated and the true population parameter, leads us to the understanding of statistical inferences (hypotheses).

Hypothesis Testing Steps

First, we must identify the parameter of interest.

Remember that a parameter always points to the population so that it will be either a population mean, population proportion, population slope, or some other population parameter.

Types of Hypothesis Tests

Then we will write a declaration of our significance test, which will include a null hypothesis statement and an alternative hypothesis.

The null hypothesis is the expected value of the population parameter, similar to the status quo, whereas the alternative hypothesis is a statement of negation of the null hypothesis as discussed by Penn State .

Next, we will calculate the desired test statistic from our random sample. This test statistic is a numerical quantity that measures the difference between the observed value and the expected value, divided by the standard error, which is the sample standard deviation.

Then we will compare this test statistic with a specified level of significance (alpha), just like we did with confidence intervals.

If the probability of yielding the sample statistic is as extreme or more extreme is smaller than our significance level, then we declare the sample statistic to be significant and reject the null hypothesis in favor of the alternative. In other words, if the probability is inside our shaded critical region then it is considered more extreme; thus, rejecting the hypothesis. But if it is outside the critical region, we will fail to reject our claim in favor of the alternative.

Null and Alternative Hypothesis

Additionally, we will also learn how to determine whether our study calls for a one or two-tailed test.

Type 1 And Type 2 Errors

Now, with all inferences and tests of significance, there is always room for error. A Type I error occurs if we reject the null hypothesis, when in actuality, the null hypothesis is true. Similarly, if we fail to reject the null hypothesis when, in reality, the null hypothesis is false, this is considered a Type II error .

Type 1 Vs. Type 2 Error

Imagine you are in a court of law, where a defendant is presumed innocent until proven guilty. What possible errors could a jury make regarding the outcome of the trial?

First, let’s state the following:

• The Null Hypothesis: The defendant is innocent.
• The Alternative Hypothesis: the defendant is guilty.

Now, a Type I Error would happen if the jury rejects the null hypothesis as false when, in reality, the null hypothesis is true. In other words, the jury finds the defendant guilty of a crime they didn’t commit.

And a Type II Error is when a jury accepts the null hypothesis as true when, in reality, the null hypothesis is false. Meaning, the defendant is found innocent of a crime they did commit.

Let’s look at an example where we put all of these ideas together.

Worked Example

Imagine we have a textile manufacturer investigating a new yarn, which claims it has a thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms.

Using a random sample of 4 specimens, the manufacturer wishes to test the claim that the mean thread elongation is less than 12 kilograms.

Write a hypothesis statement for this scenario and using a normal distribution, find the Type 1 error if the sample mean is less than 11.5 kilograms.

Type 1 Error — Example

As we can see, from the example above, the likelihood of a type I error, where the manufacturer rejects the null hypothesis when the null hypothesis is actually true, is approximately 0.023 or 2.3% likely.

Together, we will look at these two types of error and how they affect decision-making and begin to explore the notion of a probability value and how it helps us determine the validity or falsity of our claim.

Hypothesis Testing – Lesson & Examples (Video)

1 hr 17 min

• Introduction to Video: Statistical Hypotheses
• 00:00:38 – Overview of Hypothesis Testing and determining a correctly stated hypothesis testing problem (Examples #1-7)
• Exclusive Content for Members Only
• 00:14:34 – State the Null Hypothesis and the Alternative Hypothesis for each scenario (Examples #8-12)
• 00:25:46 – Hypothesis Testing Steps and Overview of Type I and Type II errors (Examples #13-14)
• 00:40:32 – Describe a Type 1 and Type 2 error (Examples #15-16)
• 00:46:32 – Overview of p-value and Tails of the Hypothesis Test
• 00:55:55 – Find the probability of a Type I and Type II error (Example #17)
• 01:06:08 – Identify null hypothesis, alternative hypothesis, and state whether the scenario is a one-tail or two-tailed test (Examples #18-21)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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11.2.1 - Five Step Hypothesis Testing Procedure

The examples on the following pages use the five step hypothesis testing procedure outlined below. This is the same procedure that we used to conduct a hypothesis test for a single mean, single proportion, difference in two means, and difference in two proportions.

When conducting a chi-square goodness-of-fit test, it makes the most sense to write the hypotheses first. The hypotheses will depend on the research question. The null hypothesis will always contain the equalities and the alternative hypothesis will be that at least one population proportion is not as specified in the null.

In order to use the chi-square distribution to approximate the sampling distribution, all expected counts must be at least five.

Where \(n\) is the total sample size and \(p_i\) is the hypothesized population proportion in the "ith" group.

To check this assumption, compute all expected counts and confirm that each is at least five.

In Step 1 you already computed the expected counts. Use this formula to compute the chi-square test statistic:

Construct a chi-square distribution with degrees of freedom equal to the number of groups minus one. The p-value is the area under that distribution to the right of the test statistic that was computed in Step 2. You can find this area by constructing a probability distribution plot in Minitab. 

Unless otherwise stated, use the standard 0.05 alpha level.

\(p \leq \alpha\) reject the null hypothesis.

\(p > \alpha\) fail to reject the null hypothesis.

Go back to the original research question and address it directly. If you rejected the null hypothesis, then there is evidence that at least one of the population proportions is not as stated in the null hypothesis. If you failed to reject the null hypothesis, then there is not enough evidence that any of the population proportions are different from what is stated in the null hypothesis. 

11.2.1.1 - Video: Cupcakes (Equal Proportions)

11.2.1.2- Cards (Equal Proportions)

Example: cards.

Research question : When randomly selecting a card from a deck with replacement, are we equally likely to select a heart, diamond, spade, and club?

I randomly selected a card from a standard deck 40 times with replacement. I pulled 13 hearts, 8 diamonds, 8 spades, and 11 clubs.

Let's use the five-step hypothesis testing procedure:

\(H_0: p_h=p_d=p_s=p_c=0.25\) \(H_a:\) at least one \(p_i\) is not as specified in the null

We can use the null hypothesis to check the assumption that all expected counts are at least 5.

\(Expected\;count=n (p_i)\)

All \(p_i\) are 0.25. \(40(0.25)=10\), thus this assumption is met and we can approximate the sampling distribution using the chi-square distribution.

 \(\chi^2=\sum \dfrac{(Observed-Expected)^2}{Expected} \)

All expected values are 10. Our observed values were 13, 8, 8, and 11.

\(\chi^2=\dfrac{(13-10)^2}{10}+\dfrac{(8-10)^2}{10}+\dfrac{(8-10)^2}{10}+\dfrac{(11-10)^2}{10}\) \(\chi^2=\dfrac{9}{10}+\dfrac{4}{10}+\dfrac{4}{10}+\dfrac{1}{10}\) \(\chi^2=1.8\)

Our sampling distribution will be a chi-square distribution.

\(df=k-1=4-1=3\)

We can find the p-value by constructing a chi-square distribution with 3 degrees of freedom to find the area to the right of \(\chi^2=1.8\)

The p-value is 0.614935

\(p>0.05\) therefore we fail to reject the null hypothesis.

There is not enough evidence to state that the proportion of hearts, diamonds, spades, and clubs that are randomly drawn from this deck are different.

What is Hypothesis Testing?

Hypothesis testing in statistics refers to analyzing an assumption about a population parameter. It is used to make an educated guess about an assumption using statistics. With the use of sample data, hypothesis testing makes an assumption about how true the assumption is for the entire population from where the sample is being taken.  

Any hypothetical statement we make may or may not be valid, and it is then our responsibility to provide evidence for its possibility. To approach any hypothesis, we follow these four simple steps that test its validity.

First, we formulate two hypothetical statements such that only one of them is true. By doing so, we can check the validity of our own hypothesis.

The next step is to formulate the statistical analysis to be followed based upon the data points.

Then we analyze the given data using our methodology.

The final step is to analyze the result and judge whether the null hypothesis will be rejected or is true.

Let’s look at several hypothesis testing examples:

It is observed that the average recovery time for a knee-surgery patient is 8 weeks. A physician believes that after successful knee surgery if the patient goes for physical therapy twice a week rather than thrice a week, the recovery period will be longer. Conduct hypothesis for this statement. 

David is a ten-year-old who finishes a 25-yard freestyle in the meantime of 16.43 seconds. David’s father bought goggles for his son, believing that it would help him to reduce his time. He then recorded a total of fifteen 25-yard freestyle for David, and the average time came out to be 16 seconds. Conduct a hypothesis.

A tire company claims their A-segment of tires have a running life of 50,000 miles before they need to be replaced, and previous studies show a standard deviation of 8,000 miles. After surveying a total of 28 tires, the mean run time came to be 46,500 miles with a standard deviation of 9800 miles. Is the claim made by the tire company consistent with the given data? Conduct hypothesis testing. 

All of the hypothesis testing examples are from real-life situations, which leads us to believe that hypothesis testing is a very practical topic indeed. It is an integral part of a researcher's study and is used in every research methodology in one way or another. 

Inferential statistics majorly deals with hypothesis testing. The research hypothesis states there is a relationship between the independent variable and dependent variable. Whereas the null hypothesis rejects this claim of any relationship between the two, our job as researchers or students is to check whether there is any relation between the two.  

Hypothesis Testing in Research Methodology

Now that we are clear about what hypothesis testing is? Let's look at the use of hypothesis testing in research methodology. Hypothesis testing is at the centre of research projects. 

What is Hypothesis Testing and Why is it Important in Research Methodology?

Often after formulating research statements, the validity of those statements need to be verified. Hypothesis testing offers a statistical approach to the researcher about the theoretical assumptions he/she made. It can be understood as quantitative results for a qualitative problem. 

(Image will be uploaded soon)

Hypothesis testing provides various techniques to test the hypothesis statement depending upon the variable and the data points. It finds its use in almost every field of research while answering statements such as whether this new medicine will work, a new testing method is appropriate, or if the outcomes of a random experiment are probable or not.

Procedure of Hypothesis Testing

To find the validity of any statement, we have to strictly follow the stepwise procedure of hypothesis testing. After stating the initial hypothesis, we have to re-write them in the form of a null and alternate hypothesis. The alternate hypothesis predicts a relationship between the variables, whereas the null hypothesis predicts no relationship between the variables.

After writing them as H 0 (null hypothesis) and H a (Alternate hypothesis), only one of the statements can be true. For example, taking the hypothesis that, on average, men are taller than women, we write the statements as:

H 0 : On average, men are not taller than women.

H a : On average, men are taller than women. 

Our next aim is to collect sample data, what we call sampling, in a way so that we can test our hypothesis. Your data should come from the concerned population for which you want to make a hypothesis. 

What is the p value in hypothesis testing? P-value gives us information about the probability of occurrence of results as extreme as observed results.

You will obtain your p-value after choosing the hypothesis testing method, which will be the guiding factor in rejecting the hypothesis. Usually, the p-value cutoff for rejecting the null hypothesis is 0.05. So anything below that, you will reject the null hypothesis. 

A low p-value means that the between-group variance is large enough that there is almost no overlapping, and it is unlikely that these came about by chance. A high p-value suggests there is a high within-group variance and low between-group variance, and any difference in the measure is due to chance only.

What is statistical hypothesis testing?

When forming conclusions through research, two sorts of errors are common: A hypothesis must be set and defined in statistics during a statistical survey or research. A statistical hypothesis is what it is called. It is, in fact, a population parameter assumption. However, it is unmistakable that this idea is always proven correct. Hypothesis testing refers to the predetermined formal procedures used by statisticians to determine whether hypotheses should be accepted or rejected. The process of selecting hypotheses for a given probability distribution based on observable data is known as hypothesis testing. Hypothesis testing is a fundamental and crucial issue in statistics. 

Why do I Need to Test it? Why not just prove an alternate one?

The quick answer is that you must as a scientist; it is part of the scientific process. Science employs a variety of methods to test or reject theories, ensuring that any new hypothesis is free of errors. One protection to ensure your research is not incorrect is to include both a null and an alternate hypothesis. The scientific community considers not incorporating the null hypothesis in your research to be poor practice. You are almost certainly setting yourself up for failure if you set out to prove another theory without first examining it. At the very least, your experiment will not be considered seriously.

Types of Hypothesis Testing

There are several types of hypothesis testing, and they are used based on the data provided. Depending on the sample size and the data given, we choose among different hypothesis testing methodologies. Here starts the use of hypothesis testing tools in research methodology.

Normality- This type of testing is used for normal distribution in a population sample. If the data points are grouped around the mean, the probability of them being above or below the mean is equally likely. Its shape resembles a bell curve that is equally distributed on either side of the mean.

T-test- This test is used when the sample size in a normally distributed population is comparatively small, and the standard deviation is unknown. Usually, if the sample size drops below 30, we use a T-test to find the confidence intervals of the population. 

Chi-Square Test- The Chi-Square test is used to test the population variance against the known or assumed value of the population variance. It is also a better choice to test the goodness of fit of a distribution of data. The two most common Chi-Square tests are the Chi-Square test of independence and the chi-square test of variance.

ANOVA- Analysis of Variance or ANOVA compares the data sets of two different populations or samples. It is similar in its use to the t-test or the Z-test, but it allows us to compare more than two sample means. ANOVA allows us to test the significance between an independent variable and a dependent variable, namely X and Y, respectively.

Z-test- It is a statistical measure to test that the means of two population samples are different when their variance is known. For a Z-test, the population is assumed to be normally distributed. A z-test is better suited in the case of large sample sizes greater than 30. This is due to the central limit theorem that as the sample size increases, the samples are considered to be distributed normally. 

FAQs on Hypothesis Testing

1. Mention the types of hypothesis Tests.

There are two types of a hypothesis tests:

Null Hypothesis: It is denoted as H₀.

Alternative Hypothesis: IT is denoted as H₁ or Hₐ.

2. What are the two errors that can be found while performing the null Hypothesis test?

While performing the null hypothesis test there is a possibility of occurring two types of errors,

Type-1: The type-1 error is denoted by (α), it is also known as the significance level. It is the rejection of the true null hypothesis. It is the error of commission.

Type-2: The type-2 error is denoted by (β). (1 - β) is known as the power test. The false null hypothesis is not rejected. It is the error of the omission. 

3. What is the p-value in hypothesis testing?

During hypothetical testing in statistics, the p-value indicates the probability of obtaining the result as extreme as observed results. A smaller p-value provides evidence to accept the alternate hypothesis. The p-value is used as a rejection point that provides the smallest level of significance at which the null hypothesis is rejected. Often p-value is calculated using the p-value tables by calculating the deviation between the observed value and the chosen reference value. 

It may also be calculated mathematically by performing integrals on all the values that fall under the curve and areas far from the reference value as the observed value relative to the total area of the curve. The p-value determines the evidence to reject the null hypothesis in hypothesis testing.

4. What is a null hypothesis?

The null hypothesis in statistics says that there is no certain difference between the population. It serves as a conjecture proposing no difference, whereas the alternate hypothesis says there is a difference. When we perform hypothesis testing, we have to state the null hypothesis and alternative hypotheses such that only one of them is ever true. 

By determining the p-value, we calculate whether the null hypothesis is to be rejected or not. If the difference between groups is low, it is merely by chance, and the null hypothesis, which states that there is no difference among groups, is true. Therefore, we have no evidence to reject the null hypothesis.

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Pokémon Go ‘Rediscover Kanto’ Special Research quest steps, rewards

Return to Gen 1 in celebration of biomes and a visual refresh

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Share All sharing options for: Pokémon Go ‘Rediscover Kanto’ Special Research quest steps, rewards

“Rediscover Kanto” is a Special Research quest in Pokémon Go which sees players revisit the first generation of Pokémon.

As well as the Special Research, there is a time limited event of the same name running April 22 to May 9, 2024 . This offers spawns of Pokémon from the Kanto region in the wild, bonus XP for completing certain activities, and boosted Friendship level increases.

The event celebrates an April 2024 visual and biome refresh in Pokémon Go , and as part of that, discovering starters Bulbasaur, Charmander, and Squirtle in their respective biomes increases their chances of being shiny.

Finally, as Pokémon Go wasn’t busy enough, the opening week of “Rediscover Kanto” coincides with 2024’s “ Sustainability Week ” event.

‘Rediscover Kanto’ Special Research quest steps and rewards

All players who log in April 22 to May 9, 2024 will receive the following Special Research for free.

Once acquired, “Rediscover Kanto” Special Research does not expire — meaning there is no need to rush through all the following quest steps.

Step 1 of 5

• Use 5 Berries to help catch Pokémon (Bulbasaur encounter)
• Feed your Buddy 5 times (Charmander encounter)
• Catch 20 Pokémon originally discovered in the Kanto region (Squirtle encounter)

Rewards: 5,000 XP, 2,500 Stardust , 1 Lucky Egg

Step 2 of 5

• Use 10 Berries to help catch Pokémon (10 Poké Balls)
• Play with your Buddy 5 times (15 Great Balls)
• Catch 30 Pokémon originally discovered in the Kanto region (10 Ultra Balls)

Rewards: 5,000 XP, 2,500 Stardust , 3 Fast TM

Step 3 of 5

• Use 15 Berries to help catch Pokémon (10 Razz Berry)
• Earn 25 hearts with your Buddy (10 Nanab Berry)
• Catch 40 Pokémon originally discovered in the Kanto region (10 Pinap Berry)

Rewards: 5,000 XP, 2,500 Stardust , 3 Charged TM

Step 4 of 5

• Use 20 Berries to help catch Pokémon (25 Bulbasaur Candy)
• Earn 4 Candy exploring with your Buddy (25 Charmander Candy)
• Catch 50 Pokémon originally discovered in the Kanto region (25 Squirtle Candy)

Rewards: 5,000 XP, 2,500 Stardust , 1 Lure

Step 5 of 5

• Use 151 Berries to catch Pokémon (15,100 XP)
• Earn 15,100 Stardust (15,100 XP)
• Catch 151 Pokémon originally discovered in the Kanto region (15,100 XP)

Rewards: 10,000 Stardust , 1 Incubator

Though it’s worth noting the steps involving catching Pokémon originally found in the Kanto region will be easier while the “Rediscover Kanto” event is still active (as, unlike the Special Research, that does have an end date), Kanto Pokémon are common enough in Pokémon Go that completing these won’t be an issue long term.

‘Rediscover Kanto’ event bonuses

Alongside the Special Research steps, the “Rediscover Kanto” event offers a handful of bonuses active April 22 to May 9, 2024:

• Increased XP for seven day PokéStop spin and Pokémon catch streaks
• Double Friendship level boost (when opening Gifts, trading, or battling together)
• Increased chance of shiny Bulbasaur, Charmander, and Squirtle when spawning in their respective biomes
• Ivysaur, Charmeleon, and Wartortle will gain Charged attacks Frenzy Plant, Blast Burn, and Hydro Cannon respectively when evolved

‘Rediscover Kanto’ Field Research tasks, rewards

Spinning a PokéStop during the event period can offer one of the following Field Research tasks:

• Power Up Pokémon 5 Times (25 Venusaur, Charizard, or Blastoise Mega Energy)
• Pokémon Go guides
• “Rediscover Kanto” Special Research
• “World of Wonder” Special Research
• Ditto disguises

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11.7: Steps in Hypothesis Testing

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Learning Objectives

• Be able to state the null hypothesis for both one-tailed and two-tailed tests
• Differentiate between a significance level and a probability level
• State the four steps involved in significance testing
• The first step is to specify the null hypothesis. For a two-tailed test, the null hypothesis is typically that a parameter equals zero although there are exceptions. A typical null hypothesis is \(\mu _1-\mu _2=0\) which is equivalent to \(\mu _1=\mu _2\). For a one-tailed test, the null hypothesis is either that a parameter is greater than or equal to zero or that a parameter is less than or equal to zero. If the prediction is that \(\mu _1\) is larger than \(\mu _2\), then the null hypothesis (the reverse of the prediction) is \(\mu _1-\mu _2\geq 0\). This is equivalent to \(\mu _1\leq \mu _2\).
• The second step is to specify the \(\alpha\) level which is also known as the significance level. Typical values are \(0.05\) and \(0.01\).
• The third step is to compute the probability value (also known as the \(p\) value). This is the probability of obtaining a sample statistic as different or more different from the parameter specified in the null hypothesis given that the null hypothesis is true.
• Finally, compare the probability value with the \(\alpha\) level. If the probability value is lower then you reject the null hypothesis. Keep in mind that rejecting the null hypothesis is not an all-or-none decision. The lower the probability value, the more confidence you can have that the null hypothesis is false. However, if your probability value is higher than the conventional \(\alpha\) level of \(0.05\), most scientists will consider your findings inconclusive. Failure to reject the null hypothesis does not constitute support for the null hypothesis. It just means you do not have sufficiently strong data to reject it.

Iowa radio analyst steps back after 42 seasons: ‘There will never be another Ed Podolak’

After 42 seasons in the Iowa radio booth, football color analyst Ed Podolak will step aside as from his game-day role, he announced Monday morning. Podolak, 76, will offer pregame analysis but no longer make the game-day trips of which he is legendary.

“I have decided that this is a good time for me to step back,” Podolak said. “I believe there is no greater honor than to be part of the Iowa Hawkeye Football team. I have loved watching these young men and coaches compete for the past 42 years. Sharing my perspective for the incredible Hawkeye fans from coast to coast has been a thrill.”

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Few people were more synonymous with a football program and the party that precedes it than Podolak was with Iowa football. Affable and energetic, Podolak entertained and informed Iowa fans for decades while remaining close to everyone inside the Kinnick Stadium fortress.

“Since his retirement from football, he has been the voice that Iowa fans have counted on for decades. Knowledgeable and passionate — always entertaining the fans across our state and across the country,” Iowa coach Kirk Ferentz said.

“There will never be another Ed Podolak.”

Hawkeye great Ed Podolak transitions out of radio booth: https://t.co/wIxqC4n8GK pic.twitter.com/OKVbN0YRf9 — HawkeyeFBNotes (@HawkeyeFBNotes) April 22, 2024

Hailing from southwest Iowa, Podolak was Iowa ’s quarterback from 1966-68. In his final year, Podolak was a first-team All-Big Ten pick and set a league record with 286 rushing yards against Northwestern . He was the Kansas City Chiefs’ second-round pick in 1969 and put together the greatest single-game postseason performance in NFL history. On Christmas Day in 1971, Podolak compiled an NFL playoff-record 350 all-purpose yards in a 27-24 double-overtime loss to Miami in an AFC divisional playoff. Podolak rushed for 85 yards and caught eight passes for 110 yards. He totaled 155 yards as a kick returner.

In nine seasons with the Chiefs, Podolak had 8,343 all-purpose yards, including 6,907 from scrimmage. He scored 40 touchdowns.

After retiring from the NFL, Podolak worked for NBC as an NFL broadcaster. In 1982, he joined WHO radio in Des Moines and offered commentary alongside Jim Zabel on Iowa football games.

“At that time, I’ve got to tell you, doing neutral broadcasts, it’s just another job,” Podolak told The Athletic . “To have a chance to come back and be part of an Iowa broadcast, I jumped at the opportunity.”

In 1997, Podolak became the sole radio color commentator when Iowa consolidated its radio networks and began working alongside Gary Dolphin. The duo had been in place for 27 years.

Podolak was not immune from public controversies. In 1997, he was arrested for public intoxication after he was found passed out on the University of Iowa’s famed Pentacrest. Then Podolak appeared in multiple inappropriate photos during a bowl trip to Tampa, Fla., in early 2009. He briefly retired, then returned a few months later after promising to remain sober.

In 2011, Podolak was struck by a vehicle while walking across the street in Scottsdale, Ariz. Alcohol was not involved, and Podolak sustained significant injuries. It was a long recovery.

Podolak routinely offered stories of his close friendships with celebrities, such as Jimmy Buffet, and he owned property in Costa Rica.

Hawkeye Sports Properties, the marketing wing of Learfield Sports, will search for Podolak’s replacement in conjunction with Iowa’s athletic department. Among the names floated as Podolak’s replacement is former players Dallas Clark, Chad Greenway, Anthony Herron, Matt Bowen and Danan Hughes.

(Photo: Des Moines Register)

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Scott Dochterman is a staff writer for The Athletic covering the Iowa Hawkeyes. He previously covered Iowa athletics for the Cedar Rapids Gazette and Land of 10. Scott also worked as an adjunct professor teaching sports journalism at the University of Iowa.

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Senate mulls next steps in Mayorkas impeachment; ocean heat is mass bleaching coral

Suzanne Nuyen

Good morning. You're reading the Up First newsletter. Subscribe here to get it delivered to your inbox, and listen to the Up First podcast for all the news you need to start your day.

Today's top news

The Democratic-led Senate will kick off the impeachment trial of Homeland Security Secretary Alejandro Mayorkas today. He's only the second Cabinet secretary to be impeached in U.S. history. Mayorkas is accused of allegedly failing to enforce immigration laws. Many Democrats have called for a motion to dismiss the trial. Senators could reach an agreement to debate the articles of impeachment tomorrow.

Department of Homeland Security Secretary Alejandro Mayorkas is the first Cabinet secretary to be impeached in roughly 150 years. As House Republicans targeted him he was involved in Senate negotiations on a bipartisan bill to change administration border policies. Go Nakamura/Getty Images hide caption

Department of Homeland Security Secretary Alejandro Mayorkas is the first Cabinet secretary to be impeached in roughly 150 years. As House Republicans targeted him he was involved in Senate negotiations on a bipartisan bill to change administration border policies.

• Utah Republican Sen. Mitt Romney tells NPR's Claudia Grisales that he would "far prefer having a debate and discussion" and that a "motion to table sets a very unfortunate constitutional precedent." Grisales says Democrats are watching moderate Republicans like Romney closely because he's one of their key swing votes to wrap this up as quickly as possible ahead of next week's congressional recess.

The U.S. is reaching out to China, hoping Beijing will use its influence on Tehran as global leaders try to avert a broader conflict in the Middle East following Iran's retaliatory attack on Israel over the weekend. But with today's announcement that the U.S. wants to triple tariffs on Chinese steel , it's unclear how far China will be willing to go along with the request from the Biden administration.

• China offers diplomatic support and an economic lifeline to Iran as one of the only countries buying Iranian oil, NPR's Jackie Northam tells Up First . China's past actions, such as when it helped broker a deal to re-establish relations between Saudi Arabia and Iran, indicate the country wants to position itself as a critical player in the region. But a specialist in China studies tells Northam that Beijing likes the idea of being a great player in the region, but it doesn't want to get involved in other countries' domestic issues that might require difficult decisions. 

Record levels of ocean heat are causing a second worldwide mass bleaching event on coral reefs in this decade. Corals are some of the world's most diverse ecosystems, and bleaching can kill them. Coral death would impact thousands of marine species as well as human communities. With mass bleaching expected to get worse as the climate keeps warming, scientists are looking for ways to help them survive.

• Some scientists have developed "super corals" that can handle heat better, NPR's Lauren Sommer reports. They want to use these corals to restore reefs hit by climate change. But they warn that this isn't a "get out of jail free" card , and these corals can only buy a little more time for reefs to hang on until humans can slow climate change. 

We, the voters

A "Stop. Shooting. People." flyer by Philadelphia Ceasefire is posted in East Germantown in Philadelphia, Pa., on March 25, 2024. Hannah Yoon for NPR hide caption

A "Stop. Shooting. People." flyer by Philadelphia Ceasefire is posted in East Germantown in Philadelphia, Pa., on March 25, 2024.

As part of the We, The Voters series, NPR is bringing you stories of gun violence and its impact on communities all week.

In southeastern Pennsylvania, children and teens deal with the threat of gun violence daily. The damage isn't just physical — they're also harmed when they lose a friend or family member to gun violence, learn that someone they know was shot, witness or even hear gunshots. Will Kiefer founded the Bench Mark Program to offer free personal training to at-risk youth. It's one of many programs aimed at trying to solve the problem of gun violence in his community.

• Read why Kiefer believes offering teens respect and a consistent support system is vital to addressing the root of gun violence among youth and learn about more programs that are creating safe spaces for kids to be kids.

The science of siblings

Sofie Elliott displays a scrapbook with photographs of herself and her sister, Simone Elliott. Kayana Szymczak/for NPR hide caption

Sofie Elliott displays a scrapbook with photographs of herself and her sister, Simone Elliott.

The Science of Siblings is a new series from NPR exploring the ways our siblings can influence us, from our money and our mental health all the way down to our very molecules

How reliable is human memory? In 2018, Sofie Elliot moved to Germany. It was the first time in 16 years she lived in the same place as her sister, Simone. As the two had long, nostalgic talks about their childhood, they realized they remembered a shared trauma in very different ways. The sisters helped each other make peace with their past through art. They've written a book called What We Thought We Remembered and choreographed a dance performance based on their story.

• Watch their performance and read their story here. Editor's note: This story contains descriptions of childhood sexual abuse.

3 things to know before you go

This March 12, 2019, file photo shows the University Village area of the University of Southern California in Los Angeles. Reed Saxon/AP hide caption

This March 12, 2019, file photo shows the University Village area of the University of Southern California in Los Angeles.

• The University of Southern California says it will no longer have its valedictorian, Asna Tabassum, speak at commencement, citing safety concerns. Some student groups, such as the organization Trojans for Israel, have criticized Tabassum's social media content about the Israel-Gaza war as "antisemitic bigotry." Others denounced USC's decision and said she should be able to speak freely.
• Are you reading this newsletter first thing in the morning, or are you a shift worker ending your day with us? A new study reveals that working nights and volatile schedules in young adulthood can leave you vulnerable to depression and poor health in middle age.
• The 2024 Olympic Games in Paris will begin in 100 days. In New York this week, Team USA hopefuls discussed their preparations . 

This newsletter was edited by Majd Al-Waheidi .

Correction April 17, 2024

An earlier version of this newsletter incorrectly stated that the University of California canceled plans for a graduation speech by this year's valedictorian, Asna Tabassum. It was actually the University of Southern California.