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Research Question Vs Hypothesis

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Research questions and hypotheses are both important elements of a research study, but they serve different purposes.

Research Question

A Research Question is a clear, concise, and specific question that a researcher asks to guide their study. Research questions are used to define the scope of the research project and to guide the collection and analysis of data. Research questions are often used in exploratory or descriptive studies, and they are open-ended in nature. Research questions should be answerable through data collection and analysis and should be linked to the research objectives or goals of the study.

A Hypothesis is a statement that predicts the relationship between two or more variables in a research study. Hypotheses are used in studies that aim to test cause-and-effect relationships between variables. A hypothesis is a tentative explanation for an observed phenomenon, and it is often derived from existing theory or previous research. Hypotheses are typically expressed as an “if-then” statement, where the “if” part refers to the independent variable, and the “then” part refers to the dependent variable. Hypotheses can be either directional (predicting the direction of the relationship between variables) or non-directional (predicting the presence of a relationship without specifying its direction).

Difference Between Research Question and Hypothesis

Here are some key differences between research questions and hypotheses:

Both Research Questions and Hypotheses are essential elements of a research study, but they serve different purposes. Research questions guide the study and help researchers define its scope, while hypotheses are used to test specific cause-and-effect relationships between variables. The choice of which to use depends on the nature of the research question, the study design, and the research objectives.

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Research Questions & Hypotheses

Generally, in quantitative studies, reviewers expect hypotheses rather than research questions. However, both research questions and hypotheses serve different purposes and can be beneficial when used together.

Research Questions

Clarify the research’s aim (farrugia et al., 2010).

• Research often begins with an interest in a topic, but a deep understanding of the subject is crucial to formulate an appropriate research question.
• Descriptive: “What factors most influence the academic achievement of senior high school students?”
• Comparative: “What is the performance difference between teaching methods A and B?”
• Relationship-based: “What is the relationship between self-efficacy and academic achievement?”
• Increasing knowledge about a subject can be achieved through systematic literature reviews, in-depth interviews with patients (and proxies), focus groups, and consultations with field experts.
• Some funding bodies, like the Canadian Institute for Health Research, recommend conducting a systematic review or a pilot study before seeking grants for full trials.
• The presence of multiple research questions in a study can complicate the design, statistical analysis, and feasibility.
• It’s advisable to focus on a single primary research question for the study.
• The primary question, clearly stated at the end of a grant proposal’s introduction, usually specifies the study population, intervention, and other relevant factors.
• The FINER criteria underscore aspects that can enhance the chances of a successful research project, including specifying the population of interest, aligning with scientific and public interest, clinical relevance, and contribution to the field, while complying with ethical and national research standards.
• The P ICOT approach is crucial in developing the study’s framework and protocol, influencing inclusion and exclusion criteria and identifying patient groups for inclusion.
• Defining the specific population, intervention, comparator, and outcome helps in selecting the right outcome measurement tool.
• The more precise the population definition and stricter the inclusion and exclusion criteria, the more significant the impact on the interpretation, applicability, and generalizability of the research findings.
• A restricted study population enhances internal validity but may limit the study’s external validity and generalizability to clinical practice.
• A broadly defined study population may better reflect clinical practice but could increase bias and reduce internal validity.
• An inadequately formulated research question can negatively impact study design, potentially leading to ineffective outcomes and affecting publication prospects.

Checklist: Good research questions for social science projects (Panke, 2018)

Research Hypotheses

Present the researcher’s predictions based on specific statements.

• These statements define the research problem or issue and indicate the direction of the researcher’s predictions.
• Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.
• The research or clinical hypothesis, derived from the research question, shapes the study’s key elements: sampling strategy, intervention, comparison, and outcome variables.
• Hypotheses can express a single outcome or multiple outcomes.
• After statistical testing, the null hypothesis is either rejected or not rejected based on whether the study’s findings are statistically significant.
• Hypothesis testing helps determine if observed findings are due to true differences and not chance.
• Hypotheses can be 1-sided (specific direction of difference) or 2-sided (presence of a difference without specifying direction).
• 2-sided hypotheses are generally preferred unless there’s a strong justification for a 1-sided hypothesis.
• A solid research hypothesis, informed by a good research question, influences the research design and paves the way for defining clear research objectives.

Types of Research Hypothesis

• In a Y-centered research design, the focus is on the dependent variable (DV) which is specified in the research question. Theories are then used to identify independent variables (IV) and explain their causal relationship with the DV.
• Example: “An increase in teacher-led instructional time (IV) is likely to improve student reading comprehension scores (DV), because extensive guided practice under expert supervision enhances learning retention and skill mastery.”
• Hypothesis Explanation: The dependent variable (student reading comprehension scores) is the focus, and the hypothesis explores how changes in the independent variable (teacher-led instructional time) affect it.
• In X-centered research designs, the independent variable is specified in the research question. Theories are used to determine potential dependent variables and the causal mechanisms at play.
• Example: “Implementing technology-based learning tools (IV) is likely to enhance student engagement in the classroom (DV), because interactive and multimedia content increases student interest and participation.”
• Hypothesis Explanation: The independent variable (technology-based learning tools) is the focus, with the hypothesis exploring its impact on a potential dependent variable (student engagement).
• Probabilistic hypotheses suggest that changes in the independent variable are likely to lead to changes in the dependent variable in a predictable manner, but not with absolute certainty.
• Example: “The more teachers engage in professional development programs (IV), the more their teaching effectiveness (DV) is likely to improve, because continuous training updates pedagogical skills and knowledge.”
• Hypothesis Explanation: This hypothesis implies a probable relationship between the extent of professional development (IV) and teaching effectiveness (DV).
• Deterministic hypotheses state that a specific change in the independent variable will lead to a specific change in the dependent variable, implying a more direct and certain relationship.
• Example: “If the school curriculum changes from traditional lecture-based methods to project-based learning (IV), then student collaboration skills (DV) are expected to improve because project-based learning inherently requires teamwork and peer interaction.”
• Hypothesis Explanation: This hypothesis presumes a direct and definite outcome (improvement in collaboration skills) resulting from a specific change in the teaching method.
• Example : “Students who identify as visual learners will score higher on tests that are presented in a visually rich format compared to tests presented in a text-only format.”
• Explanation : This hypothesis aims to describe the potential difference in test scores between visual learners taking visually rich tests and text-only tests, without implying a direct cause-and-effect relationship.
• Example : “Teaching method A will improve student performance more than method B.”
• Explanation : This hypothesis compares the effectiveness of two different teaching methods, suggesting that one will lead to better student performance than the other. It implies a direct comparison but does not necessarily establish a causal mechanism.
• Example : “Students with higher self-efficacy will show higher levels of academic achievement.”
• Explanation : This hypothesis predicts a relationship between the variable of self-efficacy and academic achievement. Unlike a causal hypothesis, it does not necessarily suggest that one variable causes changes in the other, but rather that they are related in some way.

Tips for developing research questions and hypotheses for research studies

• Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
• Learn about current trends and technological advances on the topic.
• Seek careful input from experts, mentors, colleagues, and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
• Use the FINER criteria in the development of the research question.
• Ensure that the research question follows PICOT format.
• Develop a research hypothesis from the research question.
• Ensure that the research question and objectives are answerable, feasible, and clinically relevant.

If your research hypotheses are derived from your research questions, particularly when multiple hypotheses address a single question, it’s recommended to use both research questions and hypotheses. However, if this isn’t the case, using hypotheses over research questions is advised. It’s important to note these are general guidelines, not strict rules. If you opt not to use hypotheses, consult with your supervisor for the best approach.

Farrugia, P., Petrisor, B. A., Farrokhyar, F., & Bhandari, M. (2010). Practical tips for surgical research: Research questions, hypotheses and objectives.  Canadian journal of surgery. Journal canadien de chirurgie ,  53 (4), 278–281.

Hulley, S. B., Cummings, S. R., Browner, W. S., Grady, D., & Newman, T. B. (2007). Designing clinical research. Philadelphia.

Panke, D. (2018). Research design & method selection: Making good choices in the social sciences.  Research Design & Method Selection , 1-368.

Home » Education » Difference Between Hypothesis and Research Question

Difference Between Hypothesis and Research Question

Main difference – hypothesis vs research question.

Research question and hypothesis are the foundations of a research study. Formulating the research question or developing the hypothesis can help you to decide on the approach of the research. A research question is the question the research study sets out to answer. Hypothesis is the statement the research study sets out to prove or disprove. The main difference between hypothesis and research question is that hypothesis is predictive in nature whereas research question is inquisitive in nature.

In this article, we’ll discuss,

1. What is a Hypothesis? – Meaning, Features, Characteristics, and Usage

2. What is a Research Question? – Meaning, Features, Characteristics, and Usage

What is a Hypothesis

A hypothesis is a prediction about the relationship between two or more variables. It can be described as an educated guess about what happens in an experiment. Researchers usually tend to use hypotheses when significant knowledge is already available on the subject. The hypothesis is based on this existing knowledge. After the hypothesis is developed, the researcher can develop data, analyze and use them to support or negate the hypothesis.

Not all studies have hypotheses. They are usually used in experimental quantitative research studies. They are useful in testing a specific theory or model.  A complete hypothesis always includes the variables, population and the predicted relationship between the variables. The main disadvantage of hypotheses is that their tendency to blind a researcher to unexpected results. 

What is a Research Question

A research question is the question a research study sets to answer. However, a research study can have more than one research question. The research methodologies , tools used to collect data, etc. all depend on the research question.

Research questions are often used in qualitative research, which seek to answer open-ended questions . But they can also be used in quantitative studies. Research questions can be used instead of hypotheses when there is little previous research on the subject. Research questions allow the researcher to conduct more open-ended queries, and a wide range of results can be reported.

A properly constructed research question should always be clear and concise. It should include the variables, population and the topic being studied.

Hypothesis is a tentative prediction about the relationship between two or more variables.

Research Question is the question a research study sets to answer.

Hypothesis is predictive in nature.

Research Question is inquisitive in nature.

Existing Research

Hypothesis can be used if there is significant knowledge or previous research on this subject.

Research Question can be used if there is little previous research on the subject.

Quantitative vs Qualitative

Hypothesis is mainly used in experimental quantitative studies.

Research Question can be used in both quantitative and qualitative studies.

Hypothesis doesn’t allow a wide range of outcomes.

Research Question allows a wide range of outcomes.

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Research Hypothesis vs. Research Question: What's the Difference?

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10 Significant Differences Between Research Question vs Research Hypothesis

Stating, developing and addressing a research question and developing & justifying the research hypothesis has vital significance in the research process. Both help researchers to approach PhD/research/ projects. 

“Research” is a word important for PhD which includes complex processes of finding new knowledge. A PhD candidate has to prepare a project & research proposal, identify a research gap , state a question, prepare a hypothesis and then do research. 

It includes tedious pre-preparation, lucrative research and frustrating post-preparations phases. So overall the research process though is inquisitive but can be managed by discipline and zero date planning. 

So to prepare for PhD, do it with ease and complete it joyfully; one has to understand every element correctly before starting their research. And for that tons and tons of articles and previous research must be read first. 

In addition, as we talked about, precisely identified research problem helps in stating an excellent research question or research hypothesis. Notwithstanding, students usually don’t understand what a research question or hypothesis is! 

The present blog content will focus on differences between research question and hypothesis and may let you understand what each term is. I hope this article will help you learn the PhD research process more accurately. 

Stay tuned,

Research question:  Does this article explain some common differences between a research question and a research hypothesis?

Research hypothesis:  This article explains the major differences between the research question and the research hypothesis. 

Example of research question: 

Some other examples of research questions are: , example of research hypothesis: , some of the examples of research hypotheses: , summary: research question vs hypothesis: , wrapping up: , what is a research question- simple explanation.

Put simply, a research question is a clear and concise question of the study that must be answered at the end. The answer usually is Yes/No type but clearly fills the gap. 

Let’s take an example, 

What are some common problems the LGBT community faces globally? 

Suppose, this one is one research question around which the researcher has to prepare its study. What can he or she do with this topic? 

• Conduct gatherings of the community. 
• Conduct one on one interviews. 
• Conduct News sessions 
• Study previous literature. 
• Organize some Games and invite LGBT community people to take part. 

That’s it, Nothing else he or she can do.  

No statistical analysis is required and performed for this study so the outcome of this study possibly is “problems”. And it can be solved, perhaps. Note that in-depth mathematical models, statistical analysis and other scientific studies aren’t required here. 

• What are the side effects of social media addiction on youth? 
• What are the factors that negatively impact the mental health of US people? 
• How effective carbon emission control strategies are? 

Now let’s understand the research hypothesis. 

What is a research hypothesis?- Simpler explanation

A research hypothesis is postulated in order to predict the results either negative or positive. Notedly is used so often in scientific, experimental and quantitative research.

The research hypothesis is a predictive model for getting results.  

Let’s take an example, 

The effect of time and temperature on biological sample transportation.

This study includes exclusive statistical analysis and data-driven studies to investigate the effect of various temperatures and times on biological specimen transportation. 

 Outcomes of the study will prove that at which temperature a biological sample can be safely transported. 

The outcomes are, 

• Statistics 
• The temperature which isn’t good 
• The temperature which has is best
• The tolerable zone for transportation

To interpret these kinds of results in-depth mathematical models, statistical analysis, scientific experiments and other biological studies are needed. 

• The effect of time and temperature on biological sample transportation. 
• Effect of various doses of antiviral Oseltamivir drug against viral pathogenicity. 
• Various global warming agents and their impact.  

I think you get a brief idea about how each term is different. Some of the technical differences between the research question and hypothesis are explained here. 

Differences between research question and research hypothesis: 

A research question is developed depending upon the problem or gap identified while the hypothesis is prepared based on the existing knowledge. 

More than one research question is present in a single study, while the entire research is developed around a single hypothesis that is either proven or disproven at last. 

In-depth knowledge of the subject and huge data or research studies are required to state a research hypothesis; whereas the research question can be stated using a small group of research data or knowledge. 

This indicates that the relatedness among different variables is pretty uncertain for the research question while is highly related in the case of hypothesis. 

A research question is “brief” yet includes all the important information and is open to debate which typically gives an excellent varied degree of output. 

On the other hand, the research hypothesis is a kind of formal statement- (will be proved or disproved) which assumes the relatedness between two or more variables selected for the study. 

For example,

The number of patients, population size, sample type or method selected for the study. 

Both- qualitative and quantitative studies rely on the research question, however, the hypothesis can be postulated mostly for the quantitative or experimental studies. 

Depending upon the nature of the study, the research questions are of three various types which are casual, descriptive and comparative questions while the hypotheses are causal, null, directional or non-directional. 

A thesis question must be answered; A hypothesis must be tested. 

The research question is more an elaborative research term while the hypothesis is more scientific and predictive in nature. 

Henceforth, research questions are usually used in elaborate studies in subjects such as language, arts and literature. And as we said, that’s pretty straightforward. 

The impact of the “Macbeth play” on European people. 

On the other hand, the research hypothesis is based on possibilities and probabilities whose final results either or neither prove the study and therefore include a purely scientific explanation, mathematics, equations and statistical analysis. 

Studies in science, biology and sociology rely on hypotheses (that must be tested first). 

For example, the impact of temperature and time duration on sample transportation and storage. 

If you are designing scientific research for your PhD, perhaps stating a hypothesis may help you more, although you can raise a question as well to investigate the knowledge. 

Research, as I said, is a complex process, needs the experience to design. 

Early learning may pretty helpful for students to understand the thing well. And hence this article and series of articles on this blog are meant for PhD students. 

Dr. Tushar Chauhan is a Scientist, Blogger and Scientific-writer. He has completed PhD in Genetics. Dr. Chauhan is a PhD coach and tutor.

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The Difference Between Research Questions & Hypothesis

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Research questions and hypothesis are tools used in similar ways for different research methods. Both hypothesis and research questions are written before research begins and are used to help guide the research. Hypothesis are used in deductive research, where researchers use logic and scientific findings to either prove or disprove assumptions. Heuristic research is based on experience, where researchers use observations to learn about the research subject.

Definitions

A hypothesis is defined as an educated guess, while a research question is simply the researcher wondering about the world. Hypothesis are part of the scientific research method. They are employed in research in science, sociology, mathematics and more. Research questions are part of heuristic research methods, and are also used in many fields including literature, and sociology.

As its name suggests, research questions are always written as questions. Hypothesis are written as statements preceded with the words "I predict." For example, a research question would ask, "What is the effect of heat on the effectiveness of bleach?" A hypothesis would state, "I predict heat will diminish the effectiveness of bleach."

Before Writing

Before writing a hypothesis, the researcher must determine what others have discovered about this subject. On the other hand, a research question requires less preparation, but focus and structure is critical.

For example, a researcher using a hypothesis would look up studies about bleach, information on the chemical properties of the chemical when heated and data about its effectiveness before writing the hypothesis. When using a research question, the researcher would think about how to phrase the question to ensure its scope is not too broad, too narrow or impossible to answer.

Writing Conclusions

When writing the conclusion for research conducted using a hypothesis, the researcher will write whether the hypothesis was correct or incorrect, followed by an explanation of the results of the research. The researcher using only a research question will write the answer to the question, followed by the findings of the research.

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Developing Language Teacher Autonomy through Action Research pp 45–60 Cite as

Clarifying the Research Questions or Hypotheses

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This chapter deals with the important, but often neglected, issue of establishing research questions or hypotheses, whether this is done before or (in the “real world”) often after the study has been conducted. The point is made that, in fact, research questions tend to be more common than hypotheses in action research, and guidelines are suggested for delineating such questions and deciding on appropriate question types according to the research purpose. Some example questions are provided to stimulate ideas, and an example action research study which will proceed in stages throughout the book is begun here.

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How Does a Hypothesis Differ From a Research Question?

To understand the difference between a hypothesis and a research question , we must first define the exact nature of scientific inquiry . Essentially, scientific inquiry represents a structured and systematic approach to exploration and discovery, grounded in empirical evidence and guided by the principles of logical reasoning and critical analysis. At the heart of scientific inquiry lies a fundamental commitment to unbiased observation and the rigorous assessment of information, a process that seeks to generate verifiable knowledge based on well-founded theories and methodological robustness.

A pivotal facet of successful scientific investigation is the appropriate framing of research, which serves to delineate the scope and direction of the scholarly endeavor. The meticulous articulation of research parameters not only guides investigators in the methodical exploration of a particular phenomenon but also ensures the reliability and validity of the findings derived from it. Correctly framing a research endeavor equips scholars with a clear framework, thereby preventing research ambiguities and facilitating a coherent and purposeful investigative journey.

Central to the framing of research are two interrelated yet distinct elements: the research question and the hypothesis. While the research question generally articulates the primary inquiry or set of inquiries to be addressed in a study, offering a focal point for the exploration, a hypothesis presents a tentative, testable prediction regarding the expected outcomes of the research. It is grounded in the existing literature and theoretical frameworks, serving as a provisional answer to the research question that is subject to empirical verification.

In essence, a research question seeks to identify and explore potential relationships, patterns, or trends, fostering a deep understanding of the underlying phenomena. In contrast, a hypothesis endeavors to affirm or refute predetermined assumptions through methodical testing and validation, aiming to substantiate or discredit specific theoretical postulates.

To correctly formulate and differentiate between research questions and hypotheses, let us investigate each one in further detail.

Understanding hypotheses

Crafting a well-defined hypothesis is a pivotal step in scholarly research. This task necessitates a profound grasp of the subject matter alongside a comprehensive awareness of existing scholarly dialogues and theories relevant to the topic. The hypothesis acts as a foundational pillar that directs the analytical pathways of the investigation, anchoring the exploration with grounded expectations based on existing knowledge.

In the formulation of a hypothesis, researchers must adhere to vital principles to ensure the creation of a substantial and verifiable statement. A robust hypothesis is delineated by several attributes, including precision, testability, and a congruent alignment with established research and theories. Moreover, it is formulated to facilitate empirical substantiation, aiming to either confirm or refute the established propositions through systematic investigation.

To deepen our comprehension of a hypothesis, let us examine some examples in different research contexts, illustrating how a hypothesis can shape and steer a study:

• Individuals between the ages of 40 and 60 who engage in regular physical activity are less likely to develop heart diseases than those who do not.
• Adolescents who experience traumatic events during the COVID-19 pandemic have a higher prevalence of mental health issues than those who do not.
• Remote learning hampers the development of social skills in elementary school students more than traditional classroom learning does.
• Implementing multicultural education strategies diminishes the achievement gap in multicultural classrooms.
• Marine ecosystems that experience high levels of plastic pollution exhibit a substantial reduction in biodiversity.
• Urbanization leads to a significant decrease in biodiversity in metropolitan areas due to habitat loss.
• Voting behavior in urban communities is significantly influenced by the socioeconomic status of the individuals.
• The prevalent use of social media significantly influences the formation of societal norms and behaviors in contemporary society.
• The integration of artificial intelligence in manufacturing elevates efficiency and productivity.
• An increased dependence on digital platforms compromises personal privacy and heightens the risk of data security breaches.

Each of these hypothesis examples is constructed to offer focused and testable propositions, rooted in contemporary concerns, creating a pathway for empirical verification and the generation of data-driven insights.

Understanding research questions

A critical first step in any research endeavor is the formulation of a research question, a task that requires a deep understanding of both the topic at hand and the existing scholarly landscape surrounding it. The research question serves as the beacon that guides the trajectory of the investigation, providing a focal point that centers the research activities and objectives.

In constructing a research question, scholars must be guided by certain key principles to ensure that their inquiry is both meaningful and fruitful. A well-framed research question is characterized by clarity, specificity, and a sensible alignment with existing research, which aids in building upon established foundations to foster novel insights within its scholarly domain.

To further understand the concept of research questions, let us consider some concrete examples from various fields that illustrate how a well-articulated research question can guide a research project:

• How does lifestyle affect the risk of heart disease in adults aged 40-60?
• What impact has the COVID-19 pandemic had on mental health outcomes in adolescents?
• How does remote learning impact the academic performance and social skills of elementary school students?
• What strategies can be employed to reduce the achievement gap in multicultural classrooms?
• What are the effects of plastic waste on marine ecosystems?
• How does urbanization impact biodiversity in metropolitan regions?
• How do socioeconomic factors influence voting behavior in urban communities?
• What role does social media play in shaping contemporary societal norms and behaviors?
• How does the implementation of artificial intelligence in manufacturing enhance efficiency and productivity?
• What are the implications of increasing reliance on digital platforms for personal privacy and data security?

Each of these research question examples not only maintains a clear focus on a specific topic but also stands grounded in current concerns, thereby paving the way for empirical exploration and data-driven conclusions.

Key differences between a hypothesis and a research question

In scholarly research, it is imperative to differentiate clearly between a hypothesis and a research question. The following table delineates the comparative aspects of both concepts:

When to use which

The decision to use a hypothesis or a research question largely hinges on the nature and objectives of the study. Essentially, researchers delineate between exploratory and confirmatory research . The former seeks to explore new phenomena and generate new insights, while the latter aims to verify existing theories and hypotheses. Understanding the correct circumstance for employing either a research question or a hypothesis can significantly streamline the research process, directing it towards more targeted conclusions. Let's delve into the specific situations where one may be more appropriate over the other.

Situations where a hypothesis is more appropriate

• Confirmatory Research: When the research is grounded in existing theories and seeks to validate or invalidate a specific claim or relationship.
• Quantitative Studies: In research designs that predominantly involve statistical analysis of numerical data to address the research problem.
• Experimental Research: Where controlled experiments are conducted to explore the causal relationships between different variables.
• Deductive Approaches: When the research follows a deductive approach , deriving a specific prediction from a general theory.

Situations where a research question is more appropriate

• Exploratory Research: In studies aiming to explore a new field or topic without much existing literature or established theories.
• Qualitative Research: When the study involves analyzing non-numerical data such as texts, interviews, or observational data to garner insights.
• Pilot Studies: Preliminary studies that aim to identify potential issues and refine research tools before a large-scale study.
• Inductive Approaches: Research approaches that work from specific observations to broader generalizations, aiming to develop new theories.

The interrelation between hypotheses and research questions

Understanding how a research question can give rise to hypotheses.

In scholarly inquiries, the formation of a hypothesis often finds its genesis in a well-articulated research question. This dynamic represents a pivotal juncture in research methodology, facilitating a transition from questioning to hypothesizing and setting the stage for focused analytical scrutiny. Leveraging the exploratory nature of research questions can foster the formulation of grounded hypotheses, guiding the investigative trajectory towards evidence-based conclusions.

Indeed, a well-structured research question can give rise to a series of hypotheses, each presenting a plausible answer to the research question and serving as a focal point for systematic investigation. This correlation facilitates a scaffolded approach to exploration, where researchers can build a layered understanding through a structured inquiry process.

Can a hypothesis transform into a research question?

This iterative process we have described can be envisioned as a cyclic pathway rather than a linear trajectory, wherein hypotheses, once tested and analyzed, can refine or even reformulate the initial research questions. This reflexive relationship fosters a deepened understanding and a more nuanced exploration of the research topic at hand.

To illustrate, consider a research question in the field of healthcare: "What are the primary factors influencing sleep quality in adults?" From this question, a researcher might derive several hypotheses, such as "Adults who engage in regular physical activity experience better sleep quality than those who do not." Once this hypothesis is tested, the findings could lead to further questions, fine-tuning the initial research query to delve into specific age groups, lifestyle factors, or physiological aspects, thereby perpetuating a cycle of inquiry that propels the research into deeper and more focused directions.

Research questions serve as the launchpad for scientific exploration, fostering a direction and scope that steer investigations towards relevant and focused pathways. Conversely, hypotheses act as tentative answers to these research questions, laying a grounded foundation for systematic investigations and guiding the trajectory towards evidence-based conclusions.

Selecting the right approach—whether formulating a hypothesis or crafting a research question—is not merely a procedural choice; it is a strategic decision that significantly influences the outcome of the investigation. Recognizing the interdependent and reflexive relationship between the two can foster a more robust and nuanced approach to scientific inquiry.

By embracing the cyclic pathway that intertwines questioning with hypothesizing, researchers can unlock deeper levels of understanding, paving the way for profound discoveries enriched with insight. Remember, the quality of the answers we obtain is invariably linked to the quality of the questions we ask and the hypotheses we formulate.

Header image by Luke Tanis .

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• v.53(4); 2010 Aug

Research questions, hypotheses and objectives

Patricia farrugia.

* Michael G. DeGroote School of Medicine, the

Bradley A. Petrisor

† Division of Orthopaedic Surgery and the

Forough Farrokhyar

‡ Departments of Surgery and

§ Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Ont

Mohit Bhandari

There is an increasing familiarity with the principles of evidence-based medicine in the surgical community. As surgeons become more aware of the hierarchy of evidence, grades of recommendations and the principles of critical appraisal, they develop an increasing familiarity with research design. Surgeons and clinicians are looking more and more to the literature and clinical trials to guide their practice; as such, it is becoming a responsibility of the clinical research community to attempt to answer questions that are not only well thought out but also clinically relevant. The development of the research question, including a supportive hypothesis and objectives, is a necessary key step in producing clinically relevant results to be used in evidence-based practice. A well-defined and specific research question is more likely to help guide us in making decisions about study design and population and subsequently what data will be collected and analyzed. 1

Objectives of this article

In this article, we discuss important considerations in the development of a research question and hypothesis and in defining objectives for research. By the end of this article, the reader will be able to appreciate the significance of constructing a good research question and developing hypotheses and research objectives for the successful design of a research study. The following article is divided into 3 sections: research question, research hypothesis and research objectives.

Research question

Interest in a particular topic usually begins the research process, but it is the familiarity with the subject that helps define an appropriate research question for a study. 1 Questions then arise out of a perceived knowledge deficit within a subject area or field of study. 2 Indeed, Haynes suggests that it is important to know “where the boundary between current knowledge and ignorance lies.” 1 The challenge in developing an appropriate research question is in determining which clinical uncertainties could or should be studied and also rationalizing the need for their investigation.

Increasing one’s knowledge about the subject of interest can be accomplished in many ways. Appropriate methods include systematically searching the literature, in-depth interviews and focus groups with patients (and proxies) and interviews with experts in the field. In addition, awareness of current trends and technological advances can assist with the development of research questions. 2 It is imperative to understand what has been studied about a topic to date in order to further the knowledge that has been previously gathered on a topic. Indeed, some granting institutions (e.g., Canadian Institute for Health Research) encourage applicants to conduct a systematic review of the available evidence if a recent review does not already exist and preferably a pilot or feasibility study before applying for a grant for a full trial.

In-depth knowledge about a subject may generate a number of questions. It then becomes necessary to ask whether these questions can be answered through one study or if more than one study needed. 1 Additional research questions can be developed, but several basic principles should be taken into consideration. 1 All questions, primary and secondary, should be developed at the beginning and planning stages of a study. Any additional questions should never compromise the primary question because it is the primary research question that forms the basis of the hypothesis and study objectives. It must be kept in mind that within the scope of one study, the presence of a number of research questions will affect and potentially increase the complexity of both the study design and subsequent statistical analyses, not to mention the actual feasibility of answering every question. 1 A sensible strategy is to establish a single primary research question around which to focus the study plan. 3 In a study, the primary research question should be clearly stated at the end of the introduction of the grant proposal, and it usually specifies the population to be studied, the intervention to be implemented and other circumstantial factors. 4

Hulley and colleagues 2 have suggested the use of the FINER criteria in the development of a good research question ( Box 1 ). The FINER criteria highlight useful points that may increase the chances of developing a successful research project. A good research question should specify the population of interest, be of interest to the scientific community and potentially to the public, have clinical relevance and further current knowledge in the field (and of course be compliant with the standards of ethical boards and national research standards).

FINER criteria for a good research question

Adapted with permission from Wolters Kluwer Health. 2

Whereas the FINER criteria outline the important aspects of the question in general, a useful format to use in the development of a specific research question is the PICO format — consider the population (P) of interest, the intervention (I) being studied, the comparison (C) group (or to what is the intervention being compared) and the outcome of interest (O). 3 , 5 , 6 Often timing (T) is added to PICO ( Box 2 ) — that is, “Over what time frame will the study take place?” 1 The PICOT approach helps generate a question that aids in constructing the framework of the study and subsequently in protocol development by alluding to the inclusion and exclusion criteria and identifying the groups of patients to be included. Knowing the specific population of interest, intervention (and comparator) and outcome of interest may also help the researcher identify an appropriate outcome measurement tool. 7 The more defined the population of interest, and thus the more stringent the inclusion and exclusion criteria, the greater the effect on the interpretation and subsequent applicability and generalizability of the research findings. 1 , 2 A restricted study population (and exclusion criteria) may limit bias and increase the internal validity of the study; however, this approach will limit external validity of the study and, thus, the generalizability of the findings to the practical clinical setting. Conversely, a broadly defined study population and inclusion criteria may be representative of practical clinical practice but may increase bias and reduce the internal validity of the study.

PICOT criteria 1

A poorly devised research question may affect the choice of study design, potentially lead to futile situations and, thus, hamper the chance of determining anything of clinical significance, which will then affect the potential for publication. Without devoting appropriate resources to developing the research question, the quality of the study and subsequent results may be compromised. During the initial stages of any research study, it is therefore imperative to formulate a research question that is both clinically relevant and answerable.

Research hypothesis

The primary research question should be driven by the hypothesis rather than the data. 1 , 2 That is, the research question and hypothesis should be developed before the start of the study. This sounds intuitive; however, if we take, for example, a database of information, it is potentially possible to perform multiple statistical comparisons of groups within the database to find a statistically significant association. This could then lead one to work backward from the data and develop the “question.” This is counterintuitive to the process because the question is asked specifically to then find the answer, thus collecting data along the way (i.e., in a prospective manner). Multiple statistical testing of associations from data previously collected could potentially lead to spuriously positive findings of association through chance alone. 2 Therefore, a good hypothesis must be based on a good research question at the start of a trial and, indeed, drive data collection for the study.

The research or clinical hypothesis is developed from the research question and then the main elements of the study — sampling strategy, intervention (if applicable), comparison and outcome variables — are summarized in a form that establishes the basis for testing, statistical and ultimately clinical significance. 3 For example, in a research study comparing computer-assisted acetabular component insertion versus freehand acetabular component placement in patients in need of total hip arthroplasty, the experimental group would be computer-assisted insertion and the control/conventional group would be free-hand placement. The investigative team would first state a research hypothesis. This could be expressed as a single outcome (e.g., computer-assisted acetabular component placement leads to improved functional outcome) or potentially as a complex/composite outcome; that is, more than one outcome (e.g., computer-assisted acetabular component placement leads to both improved radiographic cup placement and improved functional outcome).

However, when formally testing statistical significance, the hypothesis should be stated as a “null” hypothesis. 2 The purpose of hypothesis testing is to make an inference about the population of interest on the basis of a random sample taken from that population. The null hypothesis for the preceding research hypothesis then would be that there is no difference in mean functional outcome between the computer-assisted insertion and free-hand placement techniques. After forming the null hypothesis, the researchers would form an alternate hypothesis stating the nature of the difference, if it should appear. The alternate hypothesis would be that there is a difference in mean functional outcome between these techniques. At the end of the study, the null hypothesis is then tested statistically. If the findings of the study are not statistically significant (i.e., there is no difference in functional outcome between the groups in a statistical sense), we cannot reject the null hypothesis, whereas if the findings were significant, we can reject the null hypothesis and accept the alternate hypothesis (i.e., there is a difference in mean functional outcome between the study groups), errors in testing notwithstanding. In other words, hypothesis testing confirms or refutes the statement that the observed findings did not occur by chance alone but rather occurred because there was a true difference in outcomes between these surgical procedures. The concept of statistical hypothesis testing is complex, and the details are beyond the scope of this article.

Another important concept inherent in hypothesis testing is whether the hypotheses will be 1-sided or 2-sided. A 2-sided hypothesis states that there is a difference between the experimental group and the control group, but it does not specify in advance the expected direction of the difference. For example, we asked whether there is there an improvement in outcomes with computer-assisted surgery or whether the outcomes worse with computer-assisted surgery. We presented a 2-sided test in the above example because we did not specify the direction of the difference. A 1-sided hypothesis states a specific direction (e.g., there is an improvement in outcomes with computer-assisted surgery). A 2-sided hypothesis should be used unless there is a good justification for using a 1-sided hypothesis. As Bland and Atlman 8 stated, “One-sided hypothesis testing should never be used as a device to make a conventionally nonsignificant difference significant.”

The research hypothesis should be stated at the beginning of the study to guide the objectives for research. Whereas the investigators may state the hypothesis as being 1-sided (there is an improvement with treatment), the study and investigators must adhere to the concept of clinical equipoise. According to this principle, a clinical (or surgical) trial is ethical only if the expert community is uncertain about the relative therapeutic merits of the experimental and control groups being evaluated. 9 It means there must exist an honest and professional disagreement among expert clinicians about the preferred treatment. 9

Designing a research hypothesis is supported by a good research question and will influence the type of research design for the study. Acting on the principles of appropriate hypothesis development, the study can then confidently proceed to the development of the research objective.

Research objective

The primary objective should be coupled with the hypothesis of the study. Study objectives define the specific aims of the study and should be clearly stated in the introduction of the research protocol. 7 From our previous example and using the investigative hypothesis that there is a difference in functional outcomes between computer-assisted acetabular component placement and free-hand placement, the primary objective can be stated as follows: this study will compare the functional outcomes of computer-assisted acetabular component insertion versus free-hand placement in patients undergoing total hip arthroplasty. Note that the study objective is an active statement about how the study is going to answer the specific research question. Objectives can (and often do) state exactly which outcome measures are going to be used within their statements. They are important because they not only help guide the development of the protocol and design of study but also play a role in sample size calculations and determining the power of the study. 7 These concepts will be discussed in other articles in this series.

From the surgeon’s point of view, it is important for the study objectives to be focused on outcomes that are important to patients and clinically relevant. For example, the most methodologically sound randomized controlled trial comparing 2 techniques of distal radial fixation would have little or no clinical impact if the primary objective was to determine the effect of treatment A as compared to treatment B on intraoperative fluoroscopy time. However, if the objective was to determine the effect of treatment A as compared to treatment B on patient functional outcome at 1 year, this would have a much more significant impact on clinical decision-making. Second, more meaningful surgeon–patient discussions could ensue, incorporating patient values and preferences with the results from this study. 6 , 7 It is the precise objective and what the investigator is trying to measure that is of clinical relevance in the practical setting.

The following is an example from the literature about the relation between the research question, hypothesis and study objectives:

Study: Warden SJ, Metcalf BR, Kiss ZS, et al. Low-intensity pulsed ultrasound for chronic patellar tendinopathy: a randomized, double-blind, placebo-controlled trial. Rheumatology 2008;47:467–71.

Research question: How does low-intensity pulsed ultrasound (LIPUS) compare with a placebo device in managing the symptoms of skeletally mature patients with patellar tendinopathy?

Research hypothesis: Pain levels are reduced in patients who receive daily active-LIPUS (treatment) for 12 weeks compared with individuals who receive inactive-LIPUS (placebo).

Objective: To investigate the clinical efficacy of LIPUS in the management of patellar tendinopathy symptoms.

The development of the research question is the most important aspect of a research project. A research project can fail if the objectives and hypothesis are poorly focused and underdeveloped. Useful tips for surgical researchers are provided in Box 3 . Designing and developing an appropriate and relevant research question, hypothesis and objectives can be a difficult task. The critical appraisal of the research question used in a study is vital to the application of the findings to clinical practice. Focusing resources, time and dedication to these 3 very important tasks will help to guide a successful research project, influence interpretation of the results and affect future publication efforts.

Tips for developing research questions, hypotheses and objectives for research studies

• Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
• Learn about current trends and technological advances on the topic.
• Seek careful input from experts, mentors, colleagues and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
• Use the FINER criteria in the development of the research question.
• Ensure that the research question follows PICOT format.
• Develop a research hypothesis from the research question.
• Develop clear and well-defined primary and secondary (if needed) objectives.
• Ensure that the research question and objectives are answerable, feasible and clinically relevant.

FINER = feasible, interesting, novel, ethical, relevant; PICOT = population (patients), intervention (for intervention studies only), comparison group, outcome of interest, time.

Competing interests: No funding was received in preparation of this paper. Dr. Bhandari was funded, in part, by a Canada Research Chair, McMaster University.

Research Aims, Objectives & Questions

The “Golden Thread” Explained Simply (+ Examples)

By: David Phair (PhD) and Alexandra Shaeffer (PhD) | June 2022

The research aims , objectives and research questions (collectively called the “golden thread”) are arguably the most important thing you need to get right when you’re crafting a research proposal , dissertation or thesis . We receive questions almost every day about this “holy trinity” of research and there’s certainly a lot of confusion out there, so we’ve crafted this post to help you navigate your way through the fog.

Overview: The Golden Thread

• What is the golden thread
• What are research aims ( examples )
• What are research objectives ( examples )
• What are research questions ( examples )
• The importance of alignment in the golden thread

What is the “golden thread”?  

The golden thread simply refers to the collective research aims , research objectives , and research questions for any given project (i.e., a dissertation, thesis, or research paper ). These three elements are bundled together because it’s extremely important that they align with each other, and that the entire research project aligns with them.

Importantly, the golden thread needs to weave its way through the entirety of any research project , from start to end. In other words, it needs to be very clearly defined right at the beginning of the project (the topic ideation and proposal stage) and it needs to inform almost every decision throughout the rest of the project. For example, your research design and methodology will be heavily influenced by the golden thread (we’ll explain this in more detail later), as well as your literature review.

The research aims, objectives and research questions (the golden thread) define the focus and scope ( the delimitations ) of your research project. In other words, they help ringfence your dissertation or thesis to a relatively narrow domain, so that you can “go deep” and really dig into a specific problem or opportunity. They also help keep you on track , as they act as a litmus test for relevance. In other words, if you’re ever unsure whether to include something in your document, simply ask yourself the question, “does this contribute toward my research aims, objectives or questions?”. If it doesn’t, chances are you can drop it.

Alright, enough of the fluffy, conceptual stuff. Let’s get down to business and look at what exactly the research aims, objectives and questions are and outline a few examples to bring these concepts to life.

Research Aims: What are they?

Simply put, the research aim(s) is a statement that reflects the broad overarching goal (s) of the research project. Research aims are fairly high-level (low resolution) as they outline the general direction of the research and what it’s trying to achieve .

Research Aims: Examples  

True to the name, research aims usually start with the wording “this research aims to…”, “this research seeks to…”, and so on. For example:

“This research aims to explore employee experiences of digital transformation in retail HR.”   “This study sets out to assess the interaction between student support and self-care on well-being in engineering graduate students”  

As you can see, these research aims provide a high-level description of what the study is about and what it seeks to achieve. They’re not hyper-specific or action-oriented, but they’re clear about what the study’s focus is and what is being investigated.

Need a helping hand?

Research Objectives: What are they?

The research objectives take the research aims and make them more practical and actionable . In other words, the research objectives showcase the steps that the researcher will take to achieve the research aims.

The research objectives need to be far more specific (higher resolution) and actionable than the research aims. In fact, it’s always a good idea to craft your research objectives using the “SMART” criteria. In other words, they should be specific, measurable, achievable, relevant and time-bound”.

Research Objectives: Examples  

Let’s look at two examples of research objectives. We’ll stick with the topic and research aims we mentioned previously.  

For the digital transformation topic:

To observe the retail HR employees throughout the digital transformation. To assess employee perceptions of digital transformation in retail HR. To identify the barriers and facilitators of digital transformation in retail HR.

And for the student wellness topic:

To determine whether student self-care predicts the well-being score of engineering graduate students. To determine whether student support predicts the well-being score of engineering students. To assess the interaction between student self-care and student support when predicting well-being in engineering graduate students.

  As you can see, these research objectives clearly align with the previously mentioned research aims and effectively translate the low-resolution aims into (comparatively) higher-resolution objectives and action points . They give the research project a clear focus and present something that resembles a research-based “to-do” list.

Research Questions: What are they?

Finally, we arrive at the all-important research questions. The research questions are, as the name suggests, the key questions that your study will seek to answer . Simply put, they are the core purpose of your dissertation, thesis, or research project. You’ll present them at the beginning of your document (either in the introduction chapter or literature review chapter) and you’ll answer them at the end of your document (typically in the discussion and conclusion chapters).  

The research questions will be the driving force throughout the research process. For example, in the literature review chapter, you’ll assess the relevance of any given resource based on whether it helps you move towards answering your research questions. Similarly, your methodology and research design will be heavily influenced by the nature of your research questions. For instance, research questions that are exploratory in nature will usually make use of a qualitative approach, whereas questions that relate to measurement or relationship testing will make use of a quantitative approach.  

Let’s look at some examples of research questions to make this more tangible.

Research Questions: Examples  

Again, we’ll stick with the research aims and research objectives we mentioned previously.  

For the digital transformation topic (which would be qualitative in nature):

How do employees perceive digital transformation in retail HR? What are the barriers and facilitators of digital transformation in retail HR?  

And for the student wellness topic (which would be quantitative in nature):

Does student self-care predict the well-being scores of engineering graduate students? Does student support predict the well-being scores of engineering students? Do student self-care and student support interact when predicting well-being in engineering graduate students?  

You’ll probably notice that there’s quite a formulaic approach to this. In other words, the research questions are basically the research objectives “converted” into question format. While that is true most of the time, it’s not always the case. For example, the first research objective for the digital transformation topic was more or less a step on the path toward the other objectives, and as such, it didn’t warrant its own research question.  

So, don’t rush your research questions and sloppily reword your objectives as questions. Carefully think about what exactly you’re trying to achieve (i.e. your research aim) and the objectives you’ve set out, then craft a set of well-aligned research questions . Also, keep in mind that this can be a somewhat iterative process , where you go back and tweak research objectives and aims to ensure tight alignment throughout the golden thread.

The importance of strong alignment 

Alignment is the keyword here and we have to stress its importance . Simply put, you need to make sure that there is a very tight alignment between all three pieces of the golden thread. If your research aims and research questions don’t align, for example, your project will be pulling in different directions and will lack focus . This is a common problem students face and can cause many headaches (and tears), so be warned.

Take the time to carefully craft your research aims, objectives and research questions before you run off down the research path. Ideally, get your research supervisor/advisor to review and comment on your golden thread before you invest significant time into your project, and certainly before you start collecting data .  

Recap: The golden thread

In this post, we unpacked the golden thread of research, consisting of the research aims , research objectives and research questions . You can jump back to any section using the links below.

As always, feel free to leave a comment below – we always love to hear from you. Also, if you’re interested in 1-on-1 support, take a look at our private coaching service here.

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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38 Comments

Thank you very much for your great effort put. As an Undergraduate taking Demographic Research & Methodology, I’ve been trying so hard to understand clearly what is a Research Question, Research Aim and the Objectives in a research and the relationship between them etc. But as for now I’m thankful that you’ve solved my problem.

Well appreciated. This has helped me greatly in doing my dissertation.

An so delighted with this wonderful information thank you a lot.

so impressive i have benefited a lot looking forward to learn more on research.

I am very happy to have carefully gone through this well researched article.

Infact,I used to be phobia about anything research, because of my poor understanding of the concepts.

Now,I get to know that my research question is the same as my research objective(s) rephrased in question format.

I please I would need a follow up on the subject,as I intends to join the team of researchers. Thanks once again.

Thanks so much. This was really helpful.

I know you pepole have tried to break things into more understandable and easy format. And God bless you. Keep it up

i found this document so useful towards my study in research methods. thanks so much.

This is my 2nd read topic in your course and I should commend the simplified explanations of each part. I’m beginning to understand and absorb the use of each part of a dissertation/thesis. I’ll keep on reading your free course and might be able to avail the training course! Kudos!

Thank you! Better put that my lecture and helped to easily understand the basics which I feel often get brushed over when beginning dissertation work.

This is quite helpful. I like how the Golden thread has been explained and the needed alignment.

This is quite helpful. I really appreciate!

The article made it simple for researcher students to differentiate between three concepts.

Very innovative and educational in approach to conducting research.

I am very impressed with all these terminology, as I am a fresh student for post graduate, I am highly guided and I promised to continue making consultation when the need arise. Thanks a lot.

A very helpful piece. thanks, I really appreciate it .

Very well explained, and it might be helpful to many people like me.

Wish i had found this (and other) resource(s) at the beginning of my PhD journey… not in my writing up year… 😩 Anyways… just a quick question as i’m having some issues ordering my “golden thread”…. does it matter in what order you mention them? i.e., is it always first aims, then objectives, and finally the questions? or can you first mention the research questions and then the aims and objectives?

Thank you for a very simple explanation that builds upon the concepts in a very logical manner. Just prior to this, I read the research hypothesis article, which was equally very good. This met my primary objective.

My secondary objective was to understand the difference between research questions and research hypothesis, and in which context to use which one. However, I am still not clear on this. Can you kindly please guide?

In research, a research question is a clear and specific inquiry that the researcher wants to answer, while a research hypothesis is a tentative statement or prediction about the relationship between variables or the expected outcome of the study. Research questions are broader and guide the overall study, while hypotheses are specific and testable statements used in quantitative research. Research questions identify the problem, while hypotheses provide a focus for testing in the study.

Exactly what I need in this research journey, I look forward to more of your coaching videos.

This helped a lot. Thanks so much for the effort put into explaining it.

What data source in writing dissertation/Thesis requires?

What is data source covers when writing dessertation/thesis

This is quite useful thanks

I’m excited and thankful. I got so much value which will help me progress in my thesis.

where are the locations of the reserch statement, research objective and research question in a reserach paper? Can you write an ouline that defines their places in the researh paper?

Very helpful and important tips on Aims, Objectives and Questions.

Thank you so much for making research aim, research objectives and research question so clear. This will be helpful to me as i continue with my thesis.

Thanks much for this content. I learned a lot. And I am inspired to learn more. I am still struggling with my preparation for dissertation outline/proposal. But I consistently follow contents and tutorials and the new FB of GRAD Coach. Hope to really become confident in writing my dissertation and successfully defend it.

As a researcher and lecturer, I find splitting research goals into research aims, objectives, and questions is unnecessarily bureaucratic and confusing for students. For most biomedical research projects, including ‘real research’, 1-3 research questions will suffice (numbers may differ by discipline).

Awesome! Very important resources and presented in an informative way to easily understand the golden thread. Indeed, thank you so much.

Well explained

The blog article on research aims, objectives, and questions by Grad Coach is a clear and insightful guide that aligns with my experiences in academic research. The article effectively breaks down the often complex concepts of research aims and objectives, providing a straightforward and accessible explanation. Drawing from my own research endeavors, I appreciate the practical tips offered, such as the need for specificity and clarity when formulating research questions. The article serves as a valuable resource for students and researchers, offering a concise roadmap for crafting well-defined research goals and objectives. Whether you’re a novice or an experienced researcher, this article provides practical insights that contribute to the foundational aspects of a successful research endeavor.

A great thanks for you. it is really amazing explanation. I grasp a lot and one step up to research knowledge.

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Define Hypothesis: Unveiling the First Step in Scientific Inquiry

Master Scientific Data Visualization. Learn how to make data easier, unlock insights and captivate audiences effectively.

Welcome to the world of research, where you’ll journey through a universe brimming with questions and curiosity. In this cosmos, a hypothesis is one celestial object you can’t miss! Today’s expedition invites you on board an exploration to ‘Define Hypothesis.’ Hop in; it wouldn’t be hyperbole to state we’re about to unlock the nucleus behind every ever scientific theory and inquiry!

Definition of Hypothesis

Introduction to the concept of hypothesis.

Picture yourself as a detective solving a case. Right from inspecting clues, formulating potential theories on whodunit, putting these theories under rigorous tests until finally reaching that elusive conclusive evidence – exciting, isn’t it?

Now replace detective with researcher and voila – here comes our heavyweight term: Hypothesis. Much like how any plausible theory drives detectives’ investigations, scientific hypotheses are vital navigational compasses guiding researchers in their quest for scientific evolutions.

Explanation of What a Hypothesis Is in The Context of Research and Scientific Inquiry

A hypothesis – popularly known as an educated guess or predictive statement – represents an initial supposition or proposed explanation made on limited information but founded on validation-grounded knowledge. It forms the basis for preliminary exploration into a specific set of circumstances or natural phenomena beyond.

Formulated prior to conducting research, scientists employ hypotheses as testable conjectures to explain an observed behavior or event. Confused? Fret not. To put it simply and by example: “If I increase the frequency of watering my plants twice daily (instead of solely relying upon weather conditions), then they will grow faster.” Now that’s what we call an everyday-life hypothesis!

Remember, hypotheses are not wild guesses plucked out of thin air but rather preconceived assertions open to empirical verification. They mark the inception point for any scientific investigation and serve as cornerstones for further experiments.

Characteristics and Components of a Hypothesis

Key characteristics of a hypothesis.

Before plunging into the deep end to define a hypothesis, let’s brush up on the features that contribute to effective hypotheses. For starters, a strong hypothesis is testable. This means it must be possible for empirical evidence to either support the word hypothesis or contradict it. The proposal should also be logically consistent and grounded firmly in existing knowledge.

Further down the line, another salient feature is specificity. Good hypotheses are not broad statements but instead focus on a specific aspect or phenomenon within the intended research field. Moreover, they are typically succinct and easily understandable ensuring information isn’t lost in translation among researchers.

Moreover, any well-structured hypothesis connects the independent and dependent variables together – typically, there’s at least one independent and one dependent variable involved. These elements form a relationship where changes instigated in the independent variable affect the values observed for the dependent variable.

Lastly but importantly, a solid hypothesis often carries potential implications for future research areas and can potentially lead to further tests and studies if verified.

Elements that make up a well-formulated hypothesis

Delving deeper into what shapes up a robust hypothesis, we realize that certain crucial components determine its effectiveness.

Firstly, every good hypothesis or test has clear variables which essentially refer to specific aspects of the study subject matter being measured or manipulated during research. These aspects are segregated as:

• Independent Variable (IV): This component relates directly to what you have control over in your study.
• Dependent Variable (DV): This component consists of outcomes affected by alterations made in IV

Next comes ‘Predicted Outcome’ – what you anticipate happening as repercussions due to modification of two or more variables under scrutiny.

The ‘Testability’ factor also holds veritable importance comprising experimental procedures capable enough to refute or accept your claims.

The last element circles the argument around presenting a capacity called ‘Relationship’ correlating IV with DV believed to either causing some effect or showcasing an association.

Hence, these prime facets further accentuate your endeavor to adequately define the hypothesis.

Importance and Purpose of a Hypothesis

Understanding the Role of a Hypothesis in Research

First, let’s delve into the overarching role that hypothesis plays within research scenarios. As we define the hypothesis, you should view this as an underlying pillar or guiding star for your investigation. A well-articulated hypothesis steers your exploration by providing clarity on what specifically you aim to examine.

A meaningful analogy would be considering a hypothesis as a compass during a voyage. If research is the vast ocean where confusing whirlpools of data and evidence abound, then it can guide us in our direction rather than letting us drift aimlessly. Furthermore, the formulation of a quality hypothesis inherently demands clarity about your objectives upfront – this essentially sets your research vessel on course bearing towards effective outcomes.

Exploring Why Formulating A Hypothesis is Crucial in Scientific Investigations

So why precisely is nurturing such a detailed forecast vital?

• Structural Advantage: By proposing potential answers to posed questions via hypotheses, researchers streamline their methods and techniques. The approach undertaken depends significantly on what the suggested outcome or phenomenon might be.
• Generate Preliminary Expectations: Even if they’re proven wrong, making observations and developing models based on hypotheses often lead to more interesting inquiries or turn up unexpected findings.
• Quantifiable Predictions: More than simple conjectures, strong hypotheses are testable; they propose results expressed in measurable terms.

In essence, remember that formulating hypotheses smoothes the path towards solid conclusions by being the architect’s blueprints of robust investigations. Never underestimate the forward thrust they provide for progress within scientific inquiry!

Types of Hypotheses

Once we understand to define a hypothesis, we’ll find that hypotheses come in several types. Different classifications of plural hypotheses depend on their formulations and the nature of predictions or assumptions they lead towards – simple, complex, directional, non-directional, null, associative and causal. Let’s explore some of these.

Simple Hypothesis: Definition and Examples

A simple hypothesis is a type of prediction or an educated guess that carries one independent variable and one dependent variable. In essence, it creates a relationship between two singular entities; for instance, ‘Exercise improves memory.’ This suggests that there’s an impact (of improvement) on the ‘memory’ (dependent variable) by ‘exercise’ (independent variable).

Complex Hypothesis: Definition and Examples

On the contrary to its name mate – a simple hypothesis – a complex hypothesis involves more than just two variables. It points out multiple variables and how they interlink with each other. The effects aren’t just limited to cause-and-effect but can be interactive or combined impact-dependent variables too – for instance,’Diet and exercise affect weight loss and heart health.’ Here, diet and exercise are your independent factors influencing multifold aspects like weight loss (a dependent variable) alongside heart health(another dependent variable).

Directional Hypothesis: Definition and Examples

One might argue that the path laid by a directional hypothesis is less twisted as it predicts the directionality of an effect – whether one variable will increase or decrease another variable. An example here could be “Cutting down on alcohol will reduce liver disorders.” Here a reduction in ‘drinking alcohol’ implicitly identifies fewer occurrences of ‘liver disorders.’

Non-directional Hypothesis: Definition and Examples

Sometimes science requires open-ended answers; henceforth comes into play our non-directional hypothesis which merely stipulates that there’s going to be an impact without specifying its course – good, bad or otherwise. For example, “Exposure to secondhand smoke influences lung health.” It infers that there’s an effect on ‘lung health’ due to ‘secondhand smoke,’ without indicating if it’s an improvement or deterioration.

Null Hypothesis: Definition and Examples

The null hypothesis, often symbolized as H0, makes things pretty straight with assumptions; basically, it purports no existence of a relationship between the variables. Researchers utilize this hypothesis chiefly for statistical testing. In lay terms – “Smoking is not linked to lung cancer.” Here a nonexistence of association is suggested between ‘smoking’ and ‘lung cancer.’

Associative and Causal Hypothesis: Explanation and Examples

Now leaving the train station named Null-ville we enter into quite associative terrain where the associative hypothesis foretells ‘relationships’ but are shy when it comes to cause-effects. An instance could be “Students scoring high also tend to play chess.” These fellows here don’t claim that playing chess outrightly shoots up scores yet suggests a specific pattern.

On another spectrum brightful cause-effect claims jump in bravely shouting out not just relationships but boldly stating their causes too – “Consumption of fast food leads to obesity” is being so certain about fast food consumption (cause) escalating obesity levels(effect).

Navigating through these alternative hypotheses and variants allows us to step into researchers’ shoes better while also helps defining complex constructions bit by bit, making them simple outcomes anyone can interpret.

Developing and Testing a Hypothesis

In the world of research, it’s not uncommon to hear someone say “Let’s define hypothesis!” This term may seem complex at first glance, but its essence falls within our natural instinct to question and learn. To give structure to this innate curiosity, we form hypotheses and navigate through the rigorous process of testing them.

Process of Formulating a Hypothesis

Forming an effective hypothesis is both an art and a science. It involves finding a perfect blend between creativity and logical reasoning. Here are some simple yet essential steps you’d want to follow:

• Identify Your Research Question – The first step towards formulating a hypothesis is defining your research question based on preliminary observations or literature review.
• Conduct Thorough Literature Review – Once your question is in place, an extensive read about what has already been studied can help refine it further.
• Create Tentative Explanation – Develop a preliminary answer based on your knowledge and understanding which will serve as your tentative explanation or hypothesis.
• Refine Your Hypothesis : Refine this initial guess considering available resources for empirical testing, ethical implications, and potential outcomes.

Remember that the key is formation clarity in statement-making; overly complex language might obscure rather than clarify your central idea.

Importance of Testing a Hypothesis Through Empirical Research Methods

Testing a hypothesis isn’t simply about proving it right or wrong; it’s much more refined than that – it’s about validation and advancement of human knowledge. By applying empirical methods such as observation or experimentation, logic meets practice in real-world scenarios.

These hands-on approaches afford us precious insights into how our theories hold up under scrutiny outside the confines of abstract thought alone.

• Validity Confirmation : Empirical testing helps confirm if our predictions were correct or not, providing validation for our presumptions.
• Understanding Relationships : Testing allows us to assess the relational dynamics between variables under investigation.
• Promotes Scientific Inquiry : Empirical testing encourages a systematic and objective approach to understanding phenomena, which lies at the heart of scientific inquiry.

Consider this: hypotheses are our best-educated guesses – smart hunches rooted in what we know so far. To move beyond guessing and into knowledgeable assertion, we define hypothesis structure as one that can be empirically tested. Only then do we truly start to shape our understanding with any level of certainty.

Examples of Hypotheses in Different Fields

Indeed, it’s fundamental to understand that hypotheses are not confined to a single discipline but span across numerous fields. To better illuminate this, let’s delve into various examples.

Examples of Hypotheses in Scientific Research Studies

In the realm of scientific research studies, hypotheses play a pivotal role in shaping the basis for investigations research hypotheses and experiments. Let’s consider an elementary example: studying plant growth. A researcher might formulate the hypothesis – “If a specific type of fertilizer is used, then plants will grow more rapidly.” This hypothesis aims to validate or refute the assumption that given fertilizer perceptibly affects plant growth rate.

Another common example arises from investigating causal relationships between physical activity and heart health. The scientist may hypothesize that “Regular aerobic exercise decreases the risk of heart disease.”

Examples of Hypotheses in Social Sciences

When we transition towards social sciences, which deals with human behavior and its relation to societal constructs, our formative definitions undergo a change as well.

Imagine researchers examining how socioeconomic status influences educational attainment rates. They could pose a hypothesis saying, “High socioeconomic status positively correlates with higher levels of formal education.” This hypothesis attempts to tie economic background directly to education outcomes.

The correlation between gender diversity within workplace teams and improved business performance presents another illustration. A possible hypothesis could be – “Teams comprising diverse genders exhibit superior business performance than homogenous teams.”

Examples of Hypotheses in Psychology

Within psychology – the study dedicated to how individuals think, feel, and behave; clearly stated hypotheses serve as essential stepping stones for meaningful findings and insights.

Take, for instance, predicting performance under pressure: psychologists may propose an assumption like – “Stress triggers increased errors on complex tasks”. Or when researching cognitive development in children – they may hypothesize – “Language acquisition accelerates once children start attending school”.

Examples of Hypotheses in Medical Research

Lastly but importantly, in medical research, well-articulated hypotheses help probe pressing healthcare questions and identify effective treatments.

For instance: “Patients receiving chemotherapy experience significant weight loss”. Or regarding disease transmission during pandemics – they might propose “Regular hand sanitation reduces the risk of COVID-19 infection.”

In conclusion, these examples hopefully underline the importance and versatility of a hypothesis in scientific inquiry. Irrespective of its utilization within various research fields, a scientific hypothesis still essentially remains an educated assumption that offers direction and purpose to the investigation. Interestingly enough, each study’s defined hypothesis sets forth a path leading towards a better comprehension of our world and life within it.

Common Mistakes to Avoid when Formulating a Hypothesis

Identifying errors that researchers often make when developing a hypothesis.

Many researchers, especially those new in the field, may sometimes falter while crafting their hypotheses. Here are some frequently observed mistakes:

• Framing Vague Hypotheses : Clarity is vital when defining your hypothesis. A common pitfall involves creating an ambiguous statement which leaves room for multiple interpretations. This hinders precise data collection and analysis.
• Formulating Unfalsifiable Hypotheses : These are statements that cannot be proven false because they don’t connect to observable or measurable variables.
• Targeting Unachievable Results : Often, there is an inclination to develop complex hypotheses expecting groundbreaking findings. However, it’s crucial to limit the scope according to practical constraints and possibilities.
• Ignoring Null Hypothesis : The null hypothesis provides a means of contradiction to the alternative hypothesis being tested, making it essential for any research study.

Tips for avoiding these mistakes

After identifying the commonly made errors when forming a hypothesis, let’s now consider some proactive measures you can adopt:

• Crystallize Your Thoughts : Before you articulate your hypothesis, refine and clarify your ideas first. Define the parameters of your study clearly and ensure your proposition directly aligns with them.
• Keep It Simple : Stick with simplicity as much as possible in describing expected relationships or patterns in your research subject area. Remember: A simpler hypothesis often leads to effective testing.
• Embrace Falsifiability . To avoid making unfalsifiable claims, learn how to craft ‘If – Then’ statements articulately in your define hypothesis process.
• Remember the Null Hypothesis : Always formulate and account for a null hypothesis—a statement that negates the relationship between variables—for robust results validation.

In truth, it takes practice to strike the right balance and formulate a solid, practical hypothesis for your research. With these tips in mind, you’re better equipped to avoid common pitfalls that can compromise the quality of your investigation as they guide your approach when you define hypotheses.

Evaluating and Refining a Hypothesis

Laying out a hypothesis is merely the first stage of an intricate journey. Testing and refining this conjecture is equally pivotal in perfecting your next scientific method of undertaking. This pathway comprises evaluation for validity, and relevance, followed by refinement through research findings.

Methods for Assessing the Validity and Relevance of a Hypothesis

To define a hypothesis of meticulosity, we need to subject it to rigorous scrutiny. Utilizing statistical tests enables you to judge the validity of your hypothesis. Here’s a brief look at some key methods that can assist in assessing your theory:

• Empirical Testing : Conduct experiments or surveys as per the requirements of your study.
• Consistency Check : The hypothesis should remain consistent with other established theories and laws within its field.
• Falsifiability principle : Proposed by Karl Popper, a valid hypothesis must be capable of being proven wrong.

Let me reemphasize here, that relevance plays an integral part too especially when defining hypotheses linked with pragmatics like social sciences or business studies.

A relevant hypothesis will hold significance to not just existing knowledge but also pave the way for future work within the particular area of expertise. It should address gaps in current scientific theories while shedding light on possible solutions.

Ways to Refine and Modify a Hypothesis Based on Research Findings

Our job doesn’t end up on developing an initial proposition; it’s crucial to use findings from our research to refine that preliminary conception further. This essential process breathes life into what was once purely speculative.

While refining your conjecture can sound daunting initially, I assure you it’s nothing more complicated than diagnosing any missing links between your original theory and novel evidence you’ve discovered along this research journey.

If H0 (null hypothesis) contradicts your empirical results, then getting back onto the drafting board becomes necessary for crafting H1 (alternative hypothesis). This scientific cycle of formulating, testing then reformulating the hypotheses can continue till we eventually reach statistically significant results.

Remember, it’s important to be open-minded and responsive towards indications from your research findings. They will guide you intuitively in tweaking your working hypothesis in sync with your target goals.

Hence we must embrace this intricate art of defining a hypothesis while simultaneously embracing its dynamic nature which requires periodic refinement based upon insightful feedback from meticulous research.

Summarizing the Key Points About the Definition and Characteristics of a Hypothesis

Having delved into the concept extensively, we can confidently define a hypothesis as an informed and testable guess or prediction that acts as a guiding light in research studies and scientific investigations. When formulated correctly, it comprises two essential elements: clarity and specificity. It should be free from ambiguity, allowing other researchers to easily understand its proposed idea and the direction the study is heading.

In addition, a robust hypothesis exhibits predictability. As a researcher, you’re not only stating what you think will happen but also defining the variables in your experiment – your assumption confines your investigation’s parameters to make it manageable. Lastly, remember that any meaningful hypothesis must be verifiable — capable of being supported or refuted through data collection and analysis.

Reiterating the Importance of Hypotheses in Scientific Inquiry and Research

This discourse wouldn’t be complete without reaffirming how indispensable hypotheses are within scientific explorations and research inquiries. A conceptualized hypothesis serves as a foundational block upon which every aspect of a research project is built. It directs your observations along assumed patterns, thereby saving time during investigations.

We also need to note that formulating hypotheses promotes critical thinking skills among researchers because they require logical reasoning backed by empirical evidence rather than just empty conjectures.

Henceforth, whether you’re treading through unchartered waters of complex scientific endeavors or conducting social science research with less strict rules for predictions – keeping these insights on “define hypothesis” at hand would surely enhance your journey towards revealing valuable truths.

In essence, cultivating a comprehensive understanding of what constitutes a well-formed hypothesis not only lends credibility to our investigative ventures but also enables us to bring precision, focus, and relevance to our chosen field of exploration. The power lies in its simplistic yet profound ability to guide us from uncertainty towards concrete evidential findings – truly embodying scientific inquiry’s spirit!

Unlock the Power of Visualization with Mind the Graph: Elevate Your Hypothesis to New Heights

As a scientist, your hypothesis is the cornerstone of your research journey. But what if you could take it beyond mere words and equations, and transform it into a visual masterpiece that captivates your audience? Enter Mind the Graph , your ultimate ally in scientific visualization. With our intuitive platform, you can seamlessly translate complex hypotheses into stunning graphs, charts, and illustrations that speak volumes. Whether you are presenting at a conference, publishing a paper, or simply sharing your findings with the world, Mind the Graph empowers you to convey your hypotheses with clarity, precision, and undeniable impact. Join the scientific revolution today and let your hypotheses shine like never before with Mind the Graph.

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Fabricio Pamplona is the founder of Mind the Graph - a tool used by over 400K users in 60 countries. He has a Ph.D. and solid scientific background in Psychopharmacology and experience as a Guest Researcher at the Max Planck Institute of Psychiatry (Germany) and Researcher in D'Or Institute for Research and Education (IDOR, Brazil). Fabricio holds over 2500 citations in Google Scholar. He has 10 years of experience in small innovative businesses, with relevant experience in product design and innovation management. Connect with him on LinkedIn - Fabricio Pamplona .

Frequently asked questions

What’s the difference between a research hypothesis and a statistical hypothesis.

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

Frequently asked questions: Statistics

As the degrees of freedom increase, Student’s t distribution becomes less leptokurtic , meaning that the probability of extreme values decreases. The distribution becomes more and more similar to a standard normal distribution .

The three categories of kurtosis are:

• Mesokurtosis : An excess kurtosis of 0. Normal distributions are mesokurtic.
• Platykurtosis : A negative excess kurtosis. Platykurtic distributions are thin-tailed, meaning that they have few outliers .
• Leptokurtosis : A positive excess kurtosis. Leptokurtic distributions are fat-tailed, meaning that they have many outliers.

Probability distributions belong to two broad categories: discrete probability distributions and continuous probability distributions . Within each category, there are many types of probability distributions.

Probability is the relative frequency over an infinite number of trials.

For example, the probability of a coin landing on heads is .5, meaning that if you flip the coin an infinite number of times, it will land on heads half the time.

Since doing something an infinite number of times is impossible, relative frequency is often used as an estimate of probability. If you flip a coin 1000 times and get 507 heads, the relative frequency, .507, is a good estimate of the probability.

Categorical variables can be described by a frequency distribution. Quantitative variables can also be described by a frequency distribution, but first they need to be grouped into interval classes .

A histogram is an effective way to tell if a frequency distribution appears to have a normal distribution .

Plot a histogram and look at the shape of the bars. If the bars roughly follow a symmetrical bell or hill shape, like the example below, then the distribution is approximately normally distributed.

You can use the CHISQ.INV.RT() function to find a chi-square critical value in Excel.

For example, to calculate the chi-square critical value for a test with df = 22 and α = .05, click any blank cell and type:

=CHISQ.INV.RT(0.05,22)

You can use the qchisq() function to find a chi-square critical value in R.

For example, to calculate the chi-square critical value for a test with df = 22 and α = .05:

qchisq(p = .05, df = 22, lower.tail = FALSE)

You can use the chisq.test() function to perform a chi-square test of independence in R. Give the contingency table as a matrix for the “x” argument. For example:

m = matrix(data = c(89, 84, 86, 9, 8, 24), nrow = 3, ncol = 2)

chisq.test(x = m)

You can use the CHISQ.TEST() function to perform a chi-square test of independence in Excel. It takes two arguments, CHISQ.TEST(observed_range, expected_range), and returns the p value.

Chi-square goodness of fit tests are often used in genetics. One common application is to check if two genes are linked (i.e., if the assortment is independent). When genes are linked, the allele inherited for one gene affects the allele inherited for another gene.

Suppose that you want to know if the genes for pea texture (R = round, r = wrinkled) and color (Y = yellow, y = green) are linked. You perform a dihybrid cross between two heterozygous ( RY / ry ) pea plants. The hypotheses you’re testing with your experiment are:

• This would suggest that the genes are unlinked.
• This would suggest that the genes are linked.

You observe 100 peas:

• 78 round and yellow peas
• 6 round and green peas
• 4 wrinkled and yellow peas
• 12 wrinkled and green peas

Step 1: Calculate the expected frequencies

To calculate the expected values, you can make a Punnett square. If the two genes are unlinked, the probability of each genotypic combination is equal.

The expected phenotypic ratios are therefore 9 round and yellow: 3 round and green: 3 wrinkled and yellow: 1 wrinkled and green.

From this, you can calculate the expected phenotypic frequencies for 100 peas:

Step 2: Calculate chi-square

Χ 2 = 8.41 + 8.67 + 11.6 + 5.4 = 34.08

Step 3: Find the critical chi-square value

Since there are four groups (round and yellow, round and green, wrinkled and yellow, wrinkled and green), there are three degrees of freedom .

For a test of significance at α = .05 and df = 3, the Χ 2 critical value is 7.82.

Step 4: Compare the chi-square value to the critical value

Χ 2 = 34.08

Critical value = 7.82

The Χ 2 value is greater than the critical value .

Step 5: Decide whether the reject the null hypothesis

The Χ 2 value is greater than the critical value, so we reject the null hypothesis that the population of offspring have an equal probability of inheriting all possible genotypic combinations. There is a significant difference between the observed and expected genotypic frequencies ( p < .05).

The data supports the alternative hypothesis that the offspring do not have an equal probability of inheriting all possible genotypic combinations, which suggests that the genes are linked

You can use the chisq.test() function to perform a chi-square goodness of fit test in R. Give the observed values in the “x” argument, give the expected values in the “p” argument, and set “rescale.p” to true. For example:

chisq.test(x = c(22,30,23), p = c(25,25,25), rescale.p = TRUE)

You can use the CHISQ.TEST() function to perform a chi-square goodness of fit test in Excel. It takes two arguments, CHISQ.TEST(observed_range, expected_range), and returns the p value .

Both correlations and chi-square tests can test for relationships between two variables. However, a correlation is used when you have two quantitative variables and a chi-square test of independence is used when you have two categorical variables.

Both chi-square tests and t tests can test for differences between two groups. However, a t test is used when you have a dependent quantitative variable and an independent categorical variable (with two groups). A chi-square test of independence is used when you have two categorical variables.

The two main chi-square tests are the chi-square goodness of fit test and the chi-square test of independence .

A chi-square distribution is a continuous probability distribution . The shape of a chi-square distribution depends on its degrees of freedom , k . The mean of a chi-square distribution is equal to its degrees of freedom ( k ) and the variance is 2 k . The range is 0 to ∞.

As the degrees of freedom ( k ) increases, the chi-square distribution goes from a downward curve to a hump shape. As the degrees of freedom increases further, the hump goes from being strongly right-skewed to being approximately normal.

To find the quartiles of a probability distribution, you can use the distribution’s quantile function.

You can use the quantile() function to find quartiles in R. If your data is called “data”, then “quantile(data, prob=c(.25,.5,.75), type=1)” will return the three quartiles.

You can use the QUARTILE() function to find quartiles in Excel. If your data is in column A, then click any blank cell and type “=QUARTILE(A:A,1)” for the first quartile, “=QUARTILE(A:A,2)” for the second quartile, and “=QUARTILE(A:A,3)” for the third quartile.

You can use the PEARSON() function to calculate the Pearson correlation coefficient in Excel. If your variables are in columns A and B, then click any blank cell and type “PEARSON(A:A,B:B)”.

There is no function to directly test the significance of the correlation.

You can use the cor() function to calculate the Pearson correlation coefficient in R. To test the significance of the correlation, you can use the cor.test() function.

You should use the Pearson correlation coefficient when (1) the relationship is linear and (2) both variables are quantitative and (3) normally distributed and (4) have no outliers.

The Pearson correlation coefficient ( r ) is the most common way of measuring a linear correlation. It is a number between –1 and 1 that measures the strength and direction of the relationship between two variables.

This table summarizes the most important differences between normal distributions and Poisson distributions :

When the mean of a Poisson distribution is large (>10), it can be approximated by a normal distribution.

In the Poisson distribution formula, lambda (λ) is the mean number of events within a given interval of time or space. For example, λ = 0.748 floods per year.

The e in the Poisson distribution formula stands for the number 2.718. This number is called Euler’s constant. You can simply substitute e with 2.718 when you’re calculating a Poisson probability. Euler’s constant is a very useful number and is especially important in calculus.

The three types of skewness are:

• Right skew (also called positive skew ) . A right-skewed distribution is longer on the right side of its peak than on its left.
• Left skew (also called negative skew). A left-skewed distribution is longer on the left side of its peak than on its right.
• Zero skew. It is symmetrical and its left and right sides are mirror images.

Skewness and kurtosis are both important measures of a distribution’s shape.

• Skewness measures the asymmetry of a distribution.
• Kurtosis measures the heaviness of a distribution’s tails relative to a normal distribution .

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The t distribution was first described by statistician William Sealy Gosset under the pseudonym “Student.”

To calculate a confidence interval of a mean using the critical value of t , follow these four steps:

• Choose the significance level based on your desired confidence level. The most common confidence level is 95%, which corresponds to α = .05 in the two-tailed t table .
• Find the critical value of t in the two-tailed t table.
• Multiply the critical value of t by s / √ n .
• Add this value to the mean to calculate the upper limit of the confidence interval, and subtract this value from the mean to calculate the lower limit.

To test a hypothesis using the critical value of t , follow these four steps:

• Calculate the t value for your sample.
• Find the critical value of t in the t table .
• Determine if the (absolute) t value is greater than the critical value of t .
• Reject the null hypothesis if the sample’s t value is greater than the critical value of t . Otherwise, don’t reject the null hypothesis .

You can use the T.INV() function to find the critical value of t for one-tailed tests in Excel, and you can use the T.INV.2T() function for two-tailed tests.

You can use the qt() function to find the critical value of t in R. The function gives the critical value of t for the one-tailed test. If you want the critical value of t for a two-tailed test, divide the significance level by two.

You can use the RSQ() function to calculate R² in Excel. If your dependent variable is in column A and your independent variable is in column B, then click any blank cell and type “RSQ(A:A,B:B)”.

You can use the summary() function to view the R²  of a linear model in R. You will see the “R-squared” near the bottom of the output.

There are two formulas you can use to calculate the coefficient of determination (R²) of a simple linear regression .

The coefficient of determination (R²) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. You can interpret the R² as the proportion of variation in the dependent variable that is predicted by the statistical model.

There are three main types of missing data .

Missing completely at random (MCAR) data are randomly distributed across the variable and unrelated to other variables .

Missing at random (MAR) data are not randomly distributed but they are accounted for by other observed variables.

Missing not at random (MNAR) data systematically differ from the observed values.

To tidy up your missing data , your options usually include accepting, removing, or recreating the missing data.

• Acceptance: You leave your data as is
• Listwise or pairwise deletion: You delete all cases (participants) with missing data from analyses
• Imputation: You use other data to fill in the missing data

Missing data are important because, depending on the type, they can sometimes bias your results. This means your results may not be generalizable outside of your study because your data come from an unrepresentative sample .

Missing data , or missing values, occur when you don’t have data stored for certain variables or participants.

In any dataset, there’s usually some missing data. In quantitative research , missing values appear as blank cells in your spreadsheet.

There are two steps to calculating the geometric mean :

• Multiply all values together to get their product.
• Find the n th root of the product ( n is the number of values).

Before calculating the geometric mean, note that:

• The geometric mean can only be found for positive values.
• If any value in the data set is zero, the geometric mean is zero.

The arithmetic mean is the most commonly used type of mean and is often referred to simply as “the mean.” While the arithmetic mean is based on adding and dividing values, the geometric mean multiplies and finds the root of values.

Even though the geometric mean is a less common measure of central tendency , it’s more accurate than the arithmetic mean for percentage change and positively skewed data. The geometric mean is often reported for financial indices and population growth rates.

The geometric mean is an average that multiplies all values and finds a root of the number. For a dataset with n numbers, you find the n th root of their product.

Outliers are extreme values that differ from most values in the dataset. You find outliers at the extreme ends of your dataset.

It’s best to remove outliers only when you have a sound reason for doing so.

Some outliers represent natural variations in the population , and they should be left as is in your dataset. These are called true outliers.

Other outliers are problematic and should be removed because they represent measurement errors , data entry or processing errors, or poor sampling.

You can choose from four main ways to detect outliers :

• Sorting your values from low to high and checking minimum and maximum values
• Visualizing your data with a box plot and looking for outliers
• Using the interquartile range to create fences for your data
• Using statistical procedures to identify extreme values

Outliers can have a big impact on your statistical analyses and skew the results of any hypothesis test if they are inaccurate.

These extreme values can impact your statistical power as well, making it hard to detect a true effect if there is one.

No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.

To find the slope of the line, you’ll need to perform a regression analysis .

Correlation coefficients always range between -1 and 1.

The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.

The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.

These are the assumptions your data must meet if you want to use Pearson’s r :

• Both variables are on an interval or ratio level of measurement
• Data from both variables follow normal distributions
• Your data have no outliers
• Your data is from a random or representative sample
• You expect a linear relationship between the two variables

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

There are various ways to improve power:

• Increase the potential effect size by manipulating your independent variable more strongly,
• Increase sample size,
• Increase the significance level (alpha),
• Reduce measurement error by increasing the precision and accuracy of your measurement devices and procedures,
• Use a one-tailed test instead of a two-tailed test for t tests and z tests.

A power analysis is a calculation that helps you determine a minimum sample size for your study. It’s made up of four main components. If you know or have estimates for any three of these, you can calculate the fourth component.

• Statistical power : the likelihood that a test will detect an effect of a certain size if there is one, usually set at 80% or higher.
• Sample size : the minimum number of observations needed to observe an effect of a certain size with a given power level.
• Significance level (alpha) : the maximum risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Expected effect size : a standardized way of expressing the magnitude of the expected result of your study, usually based on similar studies or a pilot study.

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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.

The risk of making a Type II error is inversely related to the statistical power of a test. Power is the extent to which a test can correctly detect a real effect when there is one.

To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level to increase statistical power.

The risk of making a Type I error is the significance level (or alpha) that you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results ( p value ).

The significance level is usually set at 0.05 or 5%. This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true.

To reduce the Type I error probability, you can set a lower significance level.

In statistics, 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 actually false.

In statistics, power refers to the likelihood of a hypothesis test detecting a true effect if there is one. A statistically powerful test is more likely to reject a false negative (a Type II error).

If you don’t ensure enough power in your study, you may not be able to detect a statistically significant result even when it has practical significance. Your study might not have the ability to answer your research question.

While statistical significance shows that an effect exists in a study, practical significance shows that the effect is large enough to be meaningful in the real world.

Statistical significance is denoted by p -values whereas practical significance is represented by effect sizes .

There are dozens of measures of effect sizes . The most common effect sizes are Cohen’s d and Pearson’s r . Cohen’s d measures the size of the difference between two groups while Pearson’s r measures the strength of the relationship between two variables .

Effect size tells you how meaningful the relationship between variables or the difference between groups is.

A large effect size means that a research finding has practical significance, while a small effect size indicates limited practical applications.

Using descriptive and inferential statistics , you can make two types of estimates about the population : point estimates and interval estimates.

• A point estimate is a single value estimate of a parameter . For instance, a sample mean is a point estimate of a population mean.
• An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.

Both types of estimates are important for gathering a clear idea of where a parameter is likely to lie.

Standard error and standard deviation are both measures of variability . The standard deviation reflects variability within a sample, while the standard error estimates the variability across samples of a population.

The standard error of the mean , or simply standard error , indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.

To figure out whether a given number is a parameter or a statistic , ask yourself the following:

• Does the number describe a whole, complete population where every member can be reached for data collection ?
• Is it possible to collect data for this number from every member of the population in a reasonable time frame?

If the answer is yes to both questions, the number is likely to be a parameter. For small populations, data can be collected from the whole population and summarized in parameters.

If the answer is no to either of the questions, then the number is more likely to be a statistic.

The arithmetic mean is the most commonly used mean. It’s often simply called the mean or the average. But there are some other types of means you can calculate depending on your research purposes:

• Weighted mean: some values contribute more to the mean than others.
• Geometric mean : values are multiplied rather than summed up.
• Harmonic mean: reciprocals of values are used instead of the values themselves.

You can find the mean , or average, of a data set in two simple steps:

• Find the sum of the values by adding them all up.
• Divide the sum by the number of values in the data set.

This method is the same whether you are dealing with sample or population data or positive or negative numbers.

The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.

Because the median only uses one or two values, it’s unaffected by extreme outliers or non-symmetric distributions of scores. In contrast, the mean and mode can vary in skewed distributions.

To find the median , first order your data. Then calculate the middle position based on n , the number of values in your data set.

A data set can often have no mode, one mode or more than one mode – it all depends on how many different values repeat most frequently.

Your data can be:

• without any mode
• unimodal, with one mode,
• bimodal, with two modes,
• trimodal, with three modes, or
• multimodal, with four or more modes.

To find the mode :

• If your data is numerical or quantitative, order the values from low to high.
• If it is categorical, sort the values by group, in any order.

Then you simply need to identify the most frequently occurring value.

The interquartile range is the best measure of variability for skewed distributions or data sets with outliers. Because it’s based on values that come from the middle half of the distribution, it’s unlikely to be influenced by outliers .

The two most common methods for calculating interquartile range are the exclusive and inclusive methods.

The exclusive method excludes the median when identifying Q1 and Q3, while the inclusive method includes the median as a value in the data set in identifying the quartiles.

For each of these methods, you’ll need different procedures for finding the median, Q1 and Q3 depending on whether your sample size is even- or odd-numbered. The exclusive method works best for even-numbered sample sizes, while the inclusive method is often used with odd-numbered sample sizes.

While the range gives you the spread of the whole data set, the interquartile range gives you the spread of the middle half of a data set.

Homoscedasticity, or homogeneity of variances, is an assumption of equal or similar variances in different groups being compared.

This is an important assumption of parametric statistical tests because they are sensitive to any dissimilarities. Uneven variances in samples result in biased and skewed test results.

Statistical tests such as variance tests or the analysis of variance (ANOVA) use sample variance to assess group differences of populations. They use the variances of the samples to assess whether the populations they come from significantly differ from each other.

Variance is the average squared deviations from the mean, while standard deviation is the square root of this number. Both measures reflect variability in a distribution, but their units differ:

• Standard deviation is expressed in the same units as the original values (e.g., minutes or meters).
• Variance is expressed in much larger units (e.g., meters squared).

Although the units of variance are harder to intuitively understand, variance is important in statistical tests .

The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution :

• Around 68% of values are within 1 standard deviation of the mean.
• Around 95% of values are within 2 standard deviations of the mean.
• Around 99.7% of values are within 3 standard deviations of the mean.

The empirical rule is a quick way to get an overview of your data and check for any outliers or extreme values that don’t follow this pattern.

In a normal distribution , data are symmetrically distributed with no skew. Most values cluster around a central region, with values tapering off as they go further away from the center.

The measures of central tendency (mean, mode, and median) are exactly the same in a normal distribution.

The standard deviation is the average amount of variability in your data set. It tells you, on average, how far each score lies from the mean .

In normal distributions, a high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.

No. Because the range formula subtracts the lowest number from the highest number, the range is always zero or a positive number.

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution. It is the simplest measure of variability .

While central tendency tells you where most of your data points lie, variability summarizes how far apart your points from each other.

Data sets can have the same central tendency but different levels of variability or vice versa . Together, they give you a complete picture of your data.

Variability is most commonly measured with the following descriptive statistics :

• Range : the difference between the highest and lowest values
• Interquartile range : the range of the middle half of a distribution
• Standard deviation : average distance from the mean
• Variance : average of squared distances from the mean

Variability tells you how far apart points lie from each other and from the center of a distribution or a data set.

Variability is also referred to as spread, scatter or dispersion.

While interval and ratio data can both be categorized, ranked, and have equal spacing between adjacent values, only ratio scales have a true zero.

For example, temperature in Celsius or Fahrenheit is at an interval scale because zero is not the lowest possible temperature. In the Kelvin scale, a ratio scale, zero represents a total lack of thermal energy.

A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval , or which defines the threshold of statistical significance in a statistical test. It describes how far from the mean of the distribution you have to go to cover a certain amount of the total variation in the data (i.e. 90%, 95%, 99%).

If you are constructing a 95% confidence interval and are using a threshold of statistical significance of p = 0.05, then your critical value will be identical in both cases.

The t -distribution gives more probability to observations in the tails of the distribution than the standard normal distribution (a.k.a. the z -distribution).

In this way, the t -distribution is more conservative than the standard normal distribution: to reach the same level of confidence or statistical significance , you will need to include a wider range of the data.

A t -score (a.k.a. a t -value) is equivalent to the number of standard deviations away from the mean of the t -distribution .

The t -score is the test statistic used in t -tests and regression tests. It can also be used to describe how far from the mean an observation is when the data follow a t -distribution.

The t -distribution is a way of describing a set of observations where most observations fall close to the mean , and the rest of the observations make up the tails on either side. It is a type of normal distribution used for smaller sample sizes, where the variance in the data is unknown.

The t -distribution forms a bell curve when plotted on a graph. It can be described mathematically using the mean and the standard deviation .

In statistics, ordinal and nominal variables are both considered categorical variables .

Even though ordinal data can sometimes be numerical, not all mathematical operations can be performed on them.

Ordinal data has two characteristics:

• The data can be classified into different categories within a variable.
• The categories have a natural ranked order.

However, unlike with interval data, the distances between the categories are uneven or unknown.

Nominal and ordinal are two of the four levels of measurement . Nominal level data can only be classified, while ordinal level data can be classified and ordered.

Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable. These categories cannot be ordered in a meaningful way.

For example, for the nominal variable of preferred mode of transportation, you may have the categories of car, bus, train, tram or bicycle.

If your confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.

If your confidence interval for a correlation or regression includes zero, that means that if you run your experiment again there is a good chance of finding no correlation in your data.

In both of these cases, you will also find a high p -value when you run your statistical test, meaning that your results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.

If you want to calculate a confidence interval around the mean of data that is not normally distributed , you have two choices:

• Find a distribution that matches the shape of your data and use that distribution to calculate the confidence interval.
• Perform a transformation on your data to make it fit a normal distribution, and then find the confidence interval for the transformed data.

The standard normal distribution , also called the z -distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be converted into the standard normal distribution by turning the individual values into z -scores. In a z -distribution, z -scores tell you how many standard deviations away from the mean each value lies.

The z -score and t -score (aka z -value and t -value) show how many standard deviations away from the mean of the distribution you are, assuming your data follow a z -distribution or a t -distribution .

These scores are used in statistical tests to show how far from the mean of the predicted distribution your statistical estimate is. If your test produces a z -score of 2.5, this means that your estimate is 2.5 standard deviations from the predicted mean.

The predicted mean and distribution of your estimate are generated by the null hypothesis of the statistical test you are using. The more standard deviations away from the predicted mean your estimate is, the less likely it is that the estimate could have occurred under the null hypothesis .

To calculate the confidence interval , you need to know:

• The point estimate you are constructing the confidence interval for
• The critical values for the test statistic
• The standard deviation of the sample
• The sample size

Then you can plug these components into the confidence interval formula that corresponds to your data. The formula depends on the type of estimate (e.g. a mean or a proportion) and on the distribution of your data.

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way.

The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.

For example, if you are estimating a 95% confidence interval around the mean proportion of female babies born every year based on a random sample of babies, you might find an upper bound of 0.56 and a lower bound of 0.48. These are the upper and lower bounds of the confidence interval. The confidence level is 95%.

The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average.

For data from skewed distributions, the median is better than the mean because it isn’t influenced by extremely large values.

The mode is the only measure you can use for nominal or categorical data that can’t be ordered.

The measures of central tendency you can use depends on the level of measurement of your data.

• For a nominal level, you can only use the mode to find the most frequent value.
• For an ordinal level or ranked data, you can also use the median to find the value in the middle of your data set.
• For interval or ratio levels, in addition to the mode and median, you can use the mean to find the average value.

Measures of central tendency help you find the middle, or the average, of a data set.

The 3 most common measures of central tendency are the mean, median and mode.

• The mode is the most frequent value.
• The median is the middle number in an ordered data set.
• The mean is the sum of all values divided by the total number of values.

Some variables have fixed levels. For example, gender and ethnicity are always nominal level data because they cannot be ranked.

However, for other variables, you can choose the level of measurement . For example, income is a variable that can be recorded on an ordinal or a ratio scale:

• At an ordinal level , you could create 5 income groupings and code the incomes that fall within them from 1–5.
• At a ratio level , you would record exact numbers for income.

If you have a choice, the ratio level is always preferable because you can analyze data in more ways. The higher the level of measurement, the more precise your data is.

The level at which you measure a variable determines how you can analyze your data.

Depending on the level of measurement , you can perform different descriptive statistics to get an overall summary of your data and inferential statistics to see if your results support or refute your hypothesis .

Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:

• Nominal : the data can only be categorized.
• Ordinal : the data can be categorized and ranked.
• Interval : the data can be categorized and ranked, and evenly spaced.
• Ratio : the data can be categorized, ranked, evenly spaced and has a natural zero.

No. The p -value only tells you how likely the data you have observed is to have occurred under the null hypothesis .

If the p -value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.

The alpha value, or the threshold for statistical significance , is arbitrary – which value you use depends on your field of study.

In most cases, researchers use an alpha of 0.05, which means that there is a less than 5% chance that the data being tested could have occurred under the null hypothesis.

P -values are usually automatically calculated by the program you use to perform your statistical test. They can also be estimated using p -value tables for the relevant test statistic .

P -values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution.

If the test statistic is far from the mean of the null distribution, then the p -value will be small, showing that the test statistic is not likely to have occurred under the null hypothesis.

A p -value , or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test .

The test statistic you use will be determined by the statistical test.

You can choose the right statistical test by looking at what type of data you have collected and what type of relationship you want to test.

The test statistic will change based on the number of observations in your data, how variable your observations are, and how strong the underlying patterns in the data are.

For example, if one data set has higher variability while another has lower variability, the first data set will produce a test statistic closer to the null hypothesis , even if the true correlation between two variables is the same in either data set.

The formula for the test statistic depends on the statistical test being used.

Generally, the test statistic is calculated as the pattern in your data (i.e. the correlation between variables or difference between groups) divided by the variance in the data (i.e. the standard deviation ).

• Univariate statistics summarize only one variable  at a time.
• Bivariate statistics compare two variables .
• Multivariate statistics compare more than two variables .

The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset.

• Distribution refers to the frequencies of different responses.
• Measures of central tendency give you the average for each response.
• Measures of variability show you the spread or dispersion of your dataset.

Descriptive statistics summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalizable to the broader population.

In statistics, model selection is a process researchers use to compare the relative value of different statistical models and determine which one is the best fit for the observed data.

The Akaike information criterion is one of the most common methods of model selection. AIC weights the ability of the model to predict the observed data against the number of parameters the model requires to reach that level of precision.

AIC model selection can help researchers find a model that explains the observed variation in their data while avoiding overfitting.

In statistics, a model is the collection of one or more independent variables and their predicted interactions that researchers use to try to explain variation in their dependent variable.

You can test a model using a statistical test . To compare how well different models fit your data, you can use Akaike’s information criterion for model selection.

The Akaike information criterion is calculated from the maximum log-likelihood of the model and the number of parameters (K) used to reach that likelihood. The AIC function is 2K – 2(log-likelihood) .

Lower AIC values indicate a better-fit model, and a model with a delta-AIC (the difference between the two AIC values being compared) of more than -2 is considered significantly better than the model it is being compared to.

The Akaike information criterion is a mathematical test used to evaluate how well a model fits the data it is meant to describe. It penalizes models which use more independent variables (parameters) as a way to avoid over-fitting.

AIC is most often used to compare the relative goodness-of-fit among different models under consideration and to then choose the model that best fits the data.

A factorial ANOVA is any ANOVA that uses more than one categorical independent variable . A two-way ANOVA is a type of factorial ANOVA.

Some examples of factorial ANOVAs include:

• Testing the combined effects of vaccination (vaccinated or not vaccinated) and health status (healthy or pre-existing condition) on the rate of flu infection in a population.
• Testing the effects of marital status (married, single, divorced, widowed), job status (employed, self-employed, unemployed, retired), and family history (no family history, some family history) on the incidence of depression in a population.
• Testing the effects of feed type (type A, B, or C) and barn crowding (not crowded, somewhat crowded, very crowded) on the final weight of chickens in a commercial farming operation.

In ANOVA, the null hypothesis is that there is no difference among group means. If any group differs significantly from the overall group mean, then the ANOVA will report a statistically significant result.

Significant differences among group means are calculated using the F statistic, which is the ratio of the mean sum of squares (the variance explained by the independent variable) to the mean square error (the variance left over).

If the F statistic is higher than the critical value (the value of F that corresponds with your alpha value, usually 0.05), then the difference among groups is deemed statistically significant.

The only difference between one-way and two-way ANOVA is the number of independent variables . A one-way ANOVA has one independent variable, while a two-way ANOVA has two.

• One-way ANOVA : Testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka) and race finish times in a marathon.
• Two-way ANOVA : Testing the relationship between shoe brand (Nike, Adidas, Saucony, Hoka), runner age group (junior, senior, master’s), and race finishing times in a marathon.

All ANOVAs are designed to test for differences among three or more groups. If you are only testing for a difference between two groups, use a t-test instead.

Multiple linear regression is a regression model that estimates the relationship between a quantitative dependent variable and two or more independent variables using a straight line.

Linear regression most often uses mean-square error (MSE) to calculate the error of the model. MSE is calculated by:

• measuring the distance of the observed y-values from the predicted y-values at each value of x;
• squaring each of these distances;
• calculating the mean of each of the squared distances.

Linear regression fits a line to the data by finding the regression coefficient that results in the smallest MSE.

Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.

For example, the relationship between temperature and the expansion of mercury in a thermometer can be modeled using a straight line: as temperature increases, the mercury expands. This linear relationship is so certain that we can use mercury thermometers to measure temperature.

A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables).

A regression model can be used when the dependent variable is quantitative, except in the case of logistic regression, where the dependent variable is binary.

A t-test should not be used to measure differences among more than two groups, because the error structure for a t-test will underestimate the actual error when many groups are being compared.

If you want to compare the means of several groups at once, it’s best to use another statistical test such as ANOVA or a post-hoc test.

A one-sample t-test is used to compare a single population to a standard value (for example, to determine whether the average lifespan of a specific town is different from the country average).

A paired t-test is used to compare a single population before and after some experimental intervention or at two different points in time (for example, measuring student performance on a test before and after being taught the material).

A t-test measures the difference in group means divided by the pooled standard error of the two group means.

In this way, it calculates a number (the t-value) illustrating the magnitude of the difference between the two group means being compared, and estimates the likelihood that this difference exists purely by chance (p-value).

Your choice of t-test depends on whether you are studying one group or two groups, and whether you care about the direction of the difference in group means.

If you are studying one group, use a paired t-test to compare the group mean over time or after an intervention, or use a one-sample t-test to compare the group mean to a standard value. If you are studying two groups, use a two-sample t-test .

If you want to know only whether a difference exists, use a two-tailed test . If you want to know if one group mean is greater or less than the other, use a left-tailed or right-tailed one-tailed test .

A t-test is a statistical test that compares the means of two samples . It is used in hypothesis testing , with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

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