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Quantitative Research Hypothesis Examples
In general, a researcher arranges hypotheses based on the formulation of problems and theoretical studies. For quantitative research, the hypothesis used is a statistical hypothesis, meaning that the hypothesis must be tested using statistical rules. Whereas for qualitative research does not need to use statistical rules. In a quantitative study, the formulated statistical hypothesis has two forms, the null hypothesis (Ho) and the alternative hypothesis (Ha). In general, hypotheses for quantitative research have three types: Descriptive Hypothesis, Comparative Hypothesis, and Associative Hypothesis.
Descriptive Hypothesis
Descriptive hypotheses are temporary conjectures about the value of a variable, not expressing relationships or comparisons. Remember, only about the value of a variable. Statistics used to test descriptive hypotheses are sample mean tests or standard deviation tests. A researcher formulates hypothesis based on the problem formulation and theoretical study. Following are some examples of problem formulations (PF), hypotheses (H). PF: What is the percentage of junior high school mathematics mastery in the subject matter of the set? H: Junior high school mathematics teacher mastery in the subject matter reaches 70%.
PF: How good is the grade XI mastery of class XI material? H: mastery of class X material by class XI students reaches 75%.
Comparative Hypothesis
The comparative hypothesis is a temporary construct that compares the values of two variables. That is, in the comparative hypothesis, we do not determine with certainty the value of the variables we examine, but compare. Means, there are two variables that are the same, but different samples. The statistics used to test this comparative hypothesis are (assuming normality is met) using a t-test. But before that, the normality and homogeneity must be tested first. Following are some examples of problem formulations (PF), hypotheses (H). PF: Is there a difference in the problem-solving abilities of students who got X learning better than students who got Y learning? H: the problem solving ability of students who get learning X is better than students who get learning Y.
PF: Are there differences in the critical thinking skills of students who study during the day are better than students who study in the morning? H: there is no difference in the critical thinking skills of students who study in the afternoon with students who study in the morning.
The two hypothetical examples above are slightly different. In the first hypothesis, we claim that the problem solving ability of students who get learning X is better than students who get learning Y. While in the second hypothesis, there is no one-sided claim that the critical thinking skills of students who learn during the day are better or worse. We only state that there are differences. Which problem is better, it does not concern this hypothesis. The first hypothesis is a one-party test hypothesis, while the second hypothesis is called a two-party test hypothesis.
Associative Quantitative Hypothesis
The associative hypothesis is a relationship between the relationship between two variables, the dependent variable and the independent variable. The statistics are used to test this comparative hypothesis are (assuming normality is met) using Product Moment Correlation, Double Correlation, or Partial Correlation. The following are examples of problem formulations (PF), hypotheses (H). PF: Is there a relationship between student achievement and the level of student anxiety? H: there is a negative relationship between student achievement with the level of student anxiety.
PF: Is there a relationship between student learning outcomes and seating arrangements? H: there is a positive relationship between student achievement with the level of student anxiety. In the first hypothesis there are the words ‘negative relationship’. Negative relationship means inversely proportional. That is if the level of student anxiety is high, then student achievement is low. Whereas in the second hypothesis there are the words ‘positive relationship’. Positive relationship means directly proportional. It means if the seating arrangement is good, the student learning outcomes are high.
Constructing Hypotheses in Quantitative Research
Hypotheses are the testable statements linked to your research question. Hypotheses bridge the gap from the general question you intend to investigate (i.e., the research question) to concise statements of what you hypothesize the connection between your variables to be. For example, if we were studying the influence of mentoring relationships on first-generation students’ intention to remain at their university, we might have the following research question:
“Does the presence of a mentoring relationship influence first-generation students’ intentions to remain at their university?”
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Although this statement clearly articulates the construct and specific variables we intend to study, we still have not identified exactly what we are testing. We use the hypotheses to make this clear. Specifically, we create null and alternate hypotheses to indicate exactly what we intend to test. In general, the null hypothesis states that there is no observable difference or relationship, and the alternate hypothesis states that there is an observable difference or relationship. In the example above, our hypotheses would be as follows:
Null hypothesis: The presence of a mentoring relationship does not influence first-generation students’ intention to remain at their university.
Alternate hypothesis: The presence of a mentoring relationship influences first-generation students’ intention to remain at their university.
Hypotheses may be worded with or without a direction. As written above, the hypotheses do not have a direction. To give them direction, we would consult previous literature to determine how a mentoring relationship is likely to influence intention to remain in school. If the research indicates that the presence of a mentoring relationship should increase students’ connections to the university and their willingness to remain, our alternate hypothesis would state:
“The presence of a mentoring relationship increases first-generation students’ intention to remain at their university.”
If the research indicates that the presence of a mentoring relationship minimizes students’ desire to make additional connections to the university and in turn decreases their willingness to remain, our alternate hypothesis would state:
“The presence of a mentoring relationship decreases first-generation students’ intention to remain at their university.”
Once you conduct your statistical analysis you will determine if the null hypothesis should be rejected in favor of the alternate hypothesis.
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- How to Write a Strong Hypothesis | Steps & Examples
How to Write a Strong Hypothesis | Steps & Examples
Published on May 6, 2022 by Shona McCombes . Revised on December 2, 2022.
A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .
Example: Hypothesis
Daily apple consumption leads to fewer doctor’s visits.
Table of contents
What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Variables in hypotheses
Hypotheses propose a relationship between two or more types of variables .
- An independent variable is something the researcher changes or controls.
- A dependent variable is something the researcher observes and measures.
If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.
In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .
Step 1. Ask a question
Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.
Step 2. Do some preliminary research
Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.
At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.
Step 3. Formulate your hypothesis
Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.
4. Refine your hypothesis
You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:
- The relevant variables
- The specific group being studied
- The predicted outcome of the experiment or analysis
5. Phrase your hypothesis in three ways
To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.
In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.
If you are comparing two groups, the hypothesis can state what difference you expect to find between them.
6. Write a null hypothesis
If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .
- H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
- H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.
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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
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.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
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Testing Hypotheses
- What is a hypothesis?
- Significance testing
- One-tailed or two-tailed?
- Degrees of freedom
A hypothesis is a statement that we are trying to prove or disprove. It is used to express the relationship between variables and whether this relationship is significant. It is specific and offers a prediction on the results of your research question.
Your research question will lead you to developing a hypothesis, this is why your research question needs to be specific and clear.
The hypothesis will then guide you to the most appropriate techniques you should use to answer the question. They reflect the literature and theories on which you basing them. They need to be testable (i.e. measurable and practical).
Null hypothesis (H 0 ) is the proposition that there will not be a relationship between the variables you are looking at. i.e. any differences are due to chance). They always refer to the population. (Usually we don't believe this to be true.)
e.g. There is no difference in instances of illegal drug use by teenagers who are members of a gang and those who are not..
Alternative hypothesis (H A ) or ( H 1 ): this is sometimes called the research hypothesis or experimental hypothesis. It is the proposition that there will be a relationship. It is a statement of inequality between the variables you are interested in. They always refer to the sample. It is usually a declaration rather than a question and is clear, to the point and specific.
e.g. The instances of illegal drug use of teenagers who are members of a gang is different than the instances of illegal drug use of teenagers who are not gang members.
A non-directional research hypothesis - reflects an expected difference between groups but does not specify the direction of this difference (see two-tailed test).
A directional research hypothesis - reflects an expected difference between groups but does specify the direction of this difference. (see one-tailed test)
e.g. The instances of illegal drug use by teenagers who are members of a gang will be higher t han the instances of illegal drug use of teenagers who are not gang members.
Then the process of testing is to ascertain which hypothesis to believe.
It is usually easier to prove something as untrue rather than true, so looking at the null hypothesis is the usual starting point.
The process of examining the null hypothesis in light of evidence from the sample is called significance testing . It is a way of establishing a range of values in which we can establish whether the null hypothesis is true or false.
The debate over hypothesis testing
There has been discussion over whether the scientific method employed in traditional hypothesis testing is appropriate.
See below for some articles that discuss this:
- Gill, J. (1999) 'The insignificance of null hypothesis testing', Politics Research Quarterly , 52(3), pp. 647-674 .
- Wainer, H. and Robinson, D.H. (2003) 'Shaping up the practice of null hypothesis significance testing', Educational Researcher, 32(7), pp.22-30 .
- Ferguson, C.J. and Heener, M. (2012) ' A vast graveyard of undead theories: publication bias and psychological science's aversion to the null' , Perspectives on Psychological Science, 7(6), pp.555-561 .
Taken from: Salkind, N.J. (2017) Statistics for people who (think they) hate statistics. 6th edn. London: SAGE pp. 144-145.
- Null hypothesis - a simple introduction (SPSS)
A significance level defines the level when your sample evidence contradicts your null hypothesis so that your can then reject it. It is the probability of rejecting the null hypothesis when it is really true.
e.g. a significance level of 0.05 indicates that there is a 5% (or 1 in 20) risk of deciding that there is an effect when in fact there is none.
The lower the significance level that you set, then the evidence from the sample has to be stronger to be able to reject the null hypothesis.
N.B. - it is important that you set the significance level before you carry out your study and analysis.
Using Confidence Intervals
I t is possible to test the significance of your null hypothesis using Confidence Interval (see under samples and populations tab).
- if the range lies outside our predicted null hypothesis value we can reject it and accept the alternative hypothesis
The test statistic
This is another commonly used statistic
- Write down your null and alternative hypothesis
- Find the sample statistic (e.g.the mean of your sample)
- Calculate the test statistic Z score (see under Measures of spread or dispersion and Statistical tests - parametric). In this case the sample mean is compared to the population mean (assumed from the null hypothesis) and the standard error (see under Samples and population) is used rather than the standard deviation.
- Compare the test statistic with the critical values (e.g. plus or minus 1.96 for 5% significance)
- Draw a conclusion about the hypotheses - does the calculated z value lies in this critical range i.e. above 1.96 or below -1.96? If it does we can reject the null hypothesis. This would indicate that the results are significant (or an effect has been detected) - which means that if there were no difference in the population then getting a result that you have observed would be highly unlikely therefore you can reject the null hypothesis.
Type I error - this is the chance of wrongly rejecting the null hypothesis even though it is actually true, e.g. by using a 5% p level you would expect the null hypothesis to be rejected about 5% of the time when the null hypothesis is true. You could set a more stringent p level such as 1% (or 1 in 100) to be more certain of not seeing a Type I error. This, however, makes more likely another type of error (Type II) occurring.
Type II error - this is where there is an effect, but the p value you obtain is non-significant hence you don’t detect this effect.
- Statistical significance - what does it really mean?
- Statistical tables
One-tailed tests - where we know in which direction (e.g. larger or smaller) the difference between sample and population will be. It is a directional hypothesis.
Two-tailed tests - where we are looking at whether there is a difference between sample and population. This difference could be larger or smaller. This is a non-directional hypothesis.
If the difference is in the direction you have predicted (i.e. a one-tailed test) it is easier to get a significant result. Though there are arguments against using a one-tailed test (Wright and London, 2009, p. 98-99)*
*Wright, D. B. & London, K. (2009) First (and second) steps in statistics . 2nd edn. London: SAGE.
N.B. - think of the ‘tails’ as the regions at the far-end of a normal distribution. For a two-tailed test with significance level of 0.05% then 0.025% of the values would be at one end of the distribution and the other 0.025% would be at the other end of the distribution. It is the values in these ‘critical’ extreme regions where we can think about rejecting the null hypothesis and claim that there has been an effect.
Degrees of freedom ( df) is a rather difficult mathematical concept, but is needed to calculate the signifcance of certain statistical tests, such as the t-test, ANOVA and Chi-squared test.
It is broadly defined as the number of "observations" (pieces of information) in the data that are free to vary when estimating statistical parameters. (Taken from Minitab Blog ).
The higher the degrees of freedom are the more powerful and precise your estimates of the parameter (population) will be.
Typically, for a 1-sample t-test it is considered as the number of values in your sample minus 1.
For chi-squared tests with a table of rows and columns the rule is:
(Number of rows minus 1) times (number of columns minus 1)
Any accessible example to illustrate the principle of degrees of freedom using chocolates.
- You have seven chocolates in a box, each being a different type, e.g. truffle, coffee cream, caramel cluster, fudge, strawberry dream, hazelnut whirl, toffee.
- You are being good and intend to eat only one chocolate each day of the week.
- On the first day, you can choose to eat any one of the 7 chocolate types - you have a choice from all 7.
- On the second day, you can choose from the 6 remaining chocolates, on day 3 you can choose from 5 chocolates, and so on.
- On the sixth day you have a choice of the remaining 2 chocolates you haven't ate that week.
- However on the seventh day - you haven't really got any choice of chocolate - it has got to be the one you have left in your box.
- You had 7-1 = 6 days of “chocolate” freedom—in which the chocolate you ate could vary!
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The Craft of Writing a Strong Hypothesis
Table of Contents
Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.
A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.
What is a Hypothesis?
The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper.
The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.
The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.
The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.
Different Types of Hypotheses
Types of hypotheses
Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.
Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.
1. Null hypothesis
A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.
2. Alternative hypothesis
Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.
- Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
- Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'
3. Simple hypothesis
A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.
4. Complex hypothesis
In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.
5. Associative and casual hypothesis
Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.
6. Empirical hypothesis
Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.
Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher the statement after assessing a group of women who take iron tablets and charting the findings.
7. Statistical hypothesis
The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.
Characteristics of a Good Hypothesis
Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:
- A research hypothesis has to be simple yet clear to look justifiable enough.
- It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
- It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
- A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
- If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
- A hypothesis must keep and reflect the scope for further investigations and experiments.
Separating a Hypothesis from a Prediction
Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.
A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.
Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.
For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.
Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.
Finally, How to Write a Hypothesis
Quick tips on writing a hypothesis
1. Be clear about your research question
A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.
2. Carry out a recce
Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.
Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.
3. Create a 3-dimensional hypothesis
Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.
In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.
4. Write the first draft
Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.
Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.
5. Proof your hypothesis
After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.
Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.
Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.
Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.
It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.
If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.
Frequently Asked Questions (FAQs)
1. what is the definition of hypothesis.
According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.
2. What is an example of hypothesis?
The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."
3. What is an example of null hypothesis?
A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."
4. What are the types of research?
• Fundamental research
• Applied research
• Qualitative research
• Quantitative research
• Mixed research
• Exploratory research
• Longitudinal research
• Cross-sectional research
• Field research
• Laboratory research
• Fixed research
• Flexible research
• Action research
• Policy research
• Classification research
• Comparative research
• Causal research
• Inductive research
• Deductive research
5. How to write a hypothesis?
• Your hypothesis should be able to predict the relationship and outcome.
• Avoid wordiness by keeping it simple and brief.
• Your hypothesis should contain observable and testable outcomes.
• Your hypothesis should be relevant to the research question.
6. What are the 2 types of hypothesis?
• Null hypotheses are used to test the claim that "there is no difference between two groups of data".
• Alternative hypotheses test the claim that "there is a difference between two data groups".
7. Difference between research question and research hypothesis?
A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.
8. What is plural for hypothesis?
The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."
9. What is the red queen hypothesis?
The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.
10. Who is known as the father of null hypothesis?
The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.
11. When to reject null hypothesis?
You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.
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A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles
Edward barroga.
1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.
Glafera Janet Matanguihan
2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.
The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.
INTRODUCTION
Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6
It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4
There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.
DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES
A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5
On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4
Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8
Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12
CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES
Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13
There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10
TYPES OF RESEARCH QUESTIONS AND HYPOTHESES
Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .
Research questions in quantitative research
In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .
Hypotheses in quantitative research
In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .
Research questions in qualitative research
Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15
There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .
Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15
Hypotheses in qualitative research
Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1
FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES
Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14
The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14
As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.
a These statements were composed for comparison and illustrative purposes only.
b These statements are direct quotes from Higashihara and Horiuchi. 16
a This statement is a direct quote from Shimoda et al. 17
The other statements were composed for comparison and illustrative purposes only.
CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES
To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .
Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.
Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12
In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.
EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES
- EXAMPLE 1. Descriptive research question (quantitative research)
- - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
- “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
- RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
- EXAMPLE 2. Relationship research question (quantitative research)
- - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
- “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
- Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
- EXAMPLE 3. Comparative research question (quantitative research)
- - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
- “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
- RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
- STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
- EXAMPLE 4. Exploratory research question (qualitative research)
- - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
- “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
- EXAMPLE 5. Relationship research question (quantitative research)
- - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
- “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23
EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES
- EXAMPLE 1. Working hypothesis (quantitative research)
- - A hypothesis that is initially accepted for further research to produce a feasible theory
- “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
- “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
- EXAMPLE 2. Exploratory hypothesis (qualitative research)
- - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
- “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
- “Conclusion
- Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
- EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
- “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
- Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
- EXAMPLE 4. Statistical hypothesis (quantitative research)
- - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
- “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
- “Statistical Analysis
- ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27
EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS
- EXAMPLE 1. Background, hypotheses, and aims are provided
- “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
- “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
- “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
- EXAMPLE 2. Background, hypotheses, and aims are provided
- “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
- “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
- EXAMPLE 3. Background, aim, and hypothesis are provided
- “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
- “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
- “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30
Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.
Disclosure: The authors have no potential conflicts of interest to disclose.
Author Contributions:
- Conceptualization: Barroga E, Matanguihan GJ.
- Methodology: Barroga E, Matanguihan GJ.
- Writing - original draft: Barroga E, Matanguihan GJ.
- Writing - review & editing: Barroga E, Matanguihan GJ.
Introduction to Quantitative Methods in R
9 hypothesis testing.
In this chaper we’ll start to use the central limit theorem to its full potential.
Let’s quickly remind ourselves. The central limit theorem states that for any population, the means of repeatedly taken samples will approximate the population mean. Because of that, we could tell a bus of lost individuals was very very unlikely to be headed to a marathon. But we can do more, or at least we can answer quetions that come up in the real world.
Most importantely, what we can do with a knowledge of probabilities and the central limit theorem is test hypotheses. I believe this is one of the most difficult sections to understand in an intro to statistics or research methods class. It’s where we make a leap from doing math on known things (how many inches is this loaf of bread?) to the unknown (Is the baker cheating customers?)
9.1 Building Hypotheses
A hypothesis is a statement of a potential relationship, that has not yet been proven. Hypothesis testing, the topic of this chapter, is a more formalied version of testing hypotheses using statistical tests. There are other ways of testing hypothesis (if you think a squirrel is stealing food from a bird feeder, you might watch it to test that hypothesis), but we’ll focus just on the methods statistics gives us.
We use hypothesis testing as a structure in order to analyze whether relationships exist between different pheonomena or varaibles. Is there a relationship between eating breakfast as a child and height? Is there a relationship between driving and dementia? Is there a relationship between misspellings of the word pterodactyl and the release of new Jurassic Park movies? Those are all relationships we can test with the structure of hypothesis testing.
Hypothesis testing is a lot like detective work in a way (or at least the way criminal justics is supposed to be managed). What is the presumption we begin with in the legal system? Everyone is presumed innocent, until they are proven beyond a reasonable doubt to be guilty. In the context of statistics, we would call the presumption of innocence the null hypothesis. That term will be important, the null hypothesis states what our begining state of knowledge is, which is that there is no relationship between two things. Until we know a person is un-innocent,they are innocent. Untill we know there is a relationship, there is no relationship. It is generally written as H0, H for hypothesis and 0 as the starting point.
H0: The defendent is innocent.
Should our tests and evidence not disprove the null hypothesis, it will stand. We must provide evidence to disprove it. Thus, it is the prosecutors or researchers job to prove the alternative hypothesis they have proposed. We can have multiple alternative hypothesis, and we generally write them as H1, H2, and so on.
H1: The defendent committed the crime.
I should say something more about null hypotheses. Because it is the starting point of the tests, we generally aren’t concerned with proving it to be correct. As Ronald Fisher, one of the people that developed this line of statistics said, a null hypothesis, is “never proved or established, but is possibly disproved, in the course of experimentation”. It doesn’t matter if the defense attorney proves that the defendent is innocent. It can help, but that isn’t what’s important. What matters is whether the prosecutor proves the guilt. The jury can walk away with questions and be uncertain, they may even think there’s a better than 50-50 chance the accused commited the crime, but unless guilt is proven beyond a resonable doubt they are supposed to find them innocent. Our hypothesis tests works the same way.
Unless we prove that our alternative hypothesis (H1) is correct beyond a reasonable doubt, we can not reject the null hypothesis (H0). That phrase may sound slightly clunky, but it’s specific to the context of what we’re doing. We are attempting with our statistical tests to reject the null hypothesis of no relationship. If we don’t, we say that we have failed to reject the null.
One more time, because this point that will come up on a test at some point. We are attempting to disprove the null hypothesis, in order to confirm the alternative that we have proposed. If we do not, we have failed to reject the null - not proven the null, failed to reject the null.
9.1.1 An Example
What might that look like in a social science context?
Let’s say your statistics professor is always looking for ways to boost their students learning. They hypothesize that listening to classical music during lectures will help students retain the information. How could they measure that? For one thing, they could compare the grades of students that sit in class with classical music playing, against those that don’t. So to be more specific, the hypothesis would be that listening to classical music increases grades in intro to stats classes.
So what is the null hypothesis in that case, or stated differently, what is the equivalence of innocence, in the case of classical music and grades? The null hypothesis that needs to be disproven is that there is no effect of classical music.
H0: CLassical music has no effect on student grades.
And what we want to test with our hypothesis is that classical music does have an effect.
H1: Classical music improves student grades.
The professor could collect data on tests taken by one class where they played classical music and another where they didn’t If they compared the grades, they may be able to reject the null hypothesis, or they may fail. In the next section we’ll describe a bit more about what that looks like.
9.2 Rock The Hypothesis
In 2004, researchers wanted to test the impact of tv commercials that would encourage young voters to go to cast votes. In order to test the impact of tv commercials, they chose 43 tv markets (similar to cities, but slightly larger) that would see the commercials several times a day, and selected other similar tv markets that wouldn’t see the commercial. That way, they could observe whether watching the commercial had any impact on the number of 18 and 19 year olds that actually voted in the 2004 Presidential Election.
H0: TV commercials had no impact on voting rates by 18 an 19 year olds H1: TV commercials increased voting rates by 18 an 19 year olds
The data from their test is avaliable in R with the pscl package and the dataset RockTheVote.
Before we start, we should make sure we understand the data we are using. We can us nrow() to see how many observations are in the data.
THere are 85 tv markets that are studied. Next we can look at the summary statistics to get an idea of the varaibles available.
Treated is a dichotomous numerical varaible, that is 1 if the tv market watched the commercials, and is 0 if not. The mean here indicates that 49.41% of the tv markets were treated, and the remainders were untreated. In an experiment, researchers create a treatment group (those that saw the commercials) and a control group, in order to test for a difference.
r is the number of 18 and 19 year olds that voted in the 2004 election. The average tv market had 151 young registered voters that cast votes in the election.
n is the number of registered voters between the ages of 18 and 19 in each tv market.
p is the percentage of registered voters between the ages of 18 and 19 that voted in the election, meaning it could be calcualted by dividing r by n.
Strata and treatedIndex aren’t important for this exercise. The different tv markets were chosen because they were similar, so there is one market that saw the commercaisl and another similar market that didn’t. The varaible strata indicates which markets are matched together. treatedIndex indicates how many treated tv markets are above each observation. Full confession, I don’t totally understand what treatedIndex is supposed to be used for.
So to restate our hypotheses, we intend to test whether being in a tv market that saw commercails encouraging young adults to vote (treated) incaresed the voting rates among 18 and 19 year olds (p). The null hypothesis which we are attempting to reject is that there is no relationship between treated and p.
So what do we need to do to test the hypothesis that these tv commercials increased voting rates?
Last chapter we saw how similar the mean of the tour bus we found was to mean of the population of marathoners. Here, we don’t know what the population of 18 and 19 year old voters is. But we do have a control group, which we assume stands in for all 18 and 19 year olds. We’re assuming that the treated group is a random sample of the population of 18 and 19 year olds, so they should have the same exact voting rates as all other 18 and 19 year olds. However, they saw the commercials, so if there is a difference between the two groups, we can ascribe it to the commercials. Thus, we can test whether the mean voting rate among the tv markets that were treated with the commercials differs sigificantly.
Let’s start then by calculating the mean voting rate for the two groups, the treated tv markets and the control group. We can do that by using the subset() command to split RockTheVote into two data frames, based on whether the tv market was in the treated group or not.
The average voting rate among 18 and 19 year olds for the tv markets that saw the commercials is .545 or 54.5%, and the averge for the tv markets that were not treated is .516 or 51.6%. Interesting, the mean differs between the two samples.
However, as we learned last chapter, we should expet some variation between the means as we’re taking diferent samples. The means of samples will conform to a normal distribution over time, but we should expect varaiation for each individual mean. The question then is whether the mean of the treatment group differs significantly from the mean of the control group.
9.2.1 Statistical Significance
Statistical significance is important. Much of social science is driven by statistical significance. We’ll talk about the limitations later, for now though we can describe what we mean by that term. As we’ve discussed, the means of samples will differ from the mean of the population somewhat, and those means will differ by some number of standard deviations. We expect the majority of the data to fall within two standard deviations above or below the mean, and that very few will fall further away.
credit: Wikipedia
34.1 percent of the data falls within 1 standard deviation above and below the mean. That’s on both sides, so a total of 68.2 percent of the data falls between 1 standard deviation below the mean and one standard deviation above the mean. 13.6 percent of the data is between 1 and 2 standard deviations. In total, we expect 95.4 percent of the data to be within two standard deviations, either above or below the mean. - The Professor, one chapter earlier
That means, to state it a different way, that the probability that the mean of a sample taken from a population being within 2 standard deviations is .954, and the probability that it will fall further from the mean is only .046. That is fairly unlikely. So if the mean of the treatment group falls more than 2 standard deviations from the mean of the control group, that indicates it’s either a weird sample OR it isn’t from the same population. That’s what we concluded about the tour bus we found, it wasn’t drawn from the population of marathoners. And if the tv markets that saw the commercaials are that different from the markets that didn’t watch, we can conclued that they are different because of the commercials. The commercials had such a large effect on voting rates, they have changed voters.
So we know the means for the two groups, and we know they differ somewhat How do we test them to see if they come from the same poplation?
The easiest way is with what’s called a t-test, which quickly analyzes the means of two groups and determines how many standard deviations they are apart. A t-test can be used to test whether a sample comes from a certain population (marathoners, buses) or if two samples differ significantly. More often than not, you will use them to test whether two samples are different, generally with the goal of understanding whether some policy or intervention or trait makes two samples different - and the hope is to ascribe that difference to what we’re testing.
Essentially, a t-test does the work for us. Interpretting it correctly then becomes all the more important, but implementing it is straight forward with the command t.test(). Within the parentheses, we enter the two data frames and the varaible of interest. Here our two data frames are named treatment and control and the variable of interest is p
We can slowely look over the output, and discuss each term that’s produced. These will help to clarify the nuts and bolts of a t-test further.
Let’s start with the headline takeaway. We want to test whether tv commercials encouraging young adults to vote would actually make them vote in higher numbers. We see the two means that we calucalted above. 54.5% of registered 18 and 19 year olds in communities where the commercials were shown vote, while in other tv markets only 51.6% did so. Is that significant?
The answer to that quesiton is shown below P value, and the result is no. We aren’t very sure that these two groups are different, even though there is a gap between the means. We think that difference might have just been produced by chance, or the luck of the draw in creating different samples. The p value indicates the chances that we could have generated the difference between the means by chance: .1794, or roughly .18 (18%), and we aren’t willing to declare something different if we’re only 18% sure they’re different.
Why are we that uncertain? Because the test statistic isn’t very big, which helps to indicate the distance betwene our two means. The formula for calculating a test statistic is complicated, but we will discuss it. It’s a bit like your mother letting you see everything she has to do to put together thanksgiving dinner, so that you learn not to complain. We’ll see what R just did for us, so that we can more fully apprecaite how nice the software is to us.
x1 and x2 our the means for the two groups we are comparing. In this case, we’ll call everyhing with a 1 the treatment group, and 2 the control group.
s1 and s2 are the standard deviations for the treatment and control group.
And n1 and n2 are the number of observations or the sample size of both groups.
That wasn’t so bad. Then we just throw it all together!
That matches. What was all of that we just did? Essentially, we look at how far the distance between the means is, relative to the variance in the data of both.
One way to intuatively undestand what all that means is to think about what would make the test statistic larger or smaller. A larger difference in means, would produce a larger statistic. Less variance, meaning data that was more tightly clustered, would produce a larger t statistic. And a larger sample size would produce a larger t statistic. Once more, a larger difference, less variation in the data, and more data all make us more certain that differnces are real.
df stands for degrees of freedom, which is the number of independent data values in our sample.
Finally, we have the alternative hypothesis. Here it says “two.sided”. That means we were testing whether the commericals either increased the share of voting, or decreased it - we were looking at both ends or two sides of the distribution. We can specify whether we want to only look at the area above the mean, below the mean, or at both ends as we have done.
Assuming we’re seeking a difference in the means that would only be predicted by chance with a probability of .05, which test is tougher? A two-tailed test. For a two tailed test we seek a p value of .05 at both tails, splitting it with .025 above the mean and .025 below the mean. A one-tailed test places all .05 above or below the mean. Below, the green lines show the cut off at both ends if we only look for the difference in one tail, whereas the red line shows what happens when we look in both tails. This is all to explain why the default option is two.sided, and to generally tell you to let the default stand.
That, was a lot. It might help to walk through another example a bit quicker where we just lay out the basics of a t-test. We can use some polling data for the 1992 election, that asked people who they voted for along with a few demographic questions.
The vote varaible shows who they voters voted for. dem and rep indicate the registered party of voters and females records their gender. The questions persfinance and natlecon indicate whether the respondont thought their personl finances had improved over the previous 4 years (Bush’s first term) and whether the national economy was improving. The other three varaibles require more math than we need right now, but they generally record how distant the voters views are from the candidates.
Let’s see whether personal finances drove people to vote for Bush’s relection.
H0: Personal finance made no difference in the election H1: Voters that felt their personal fiances improved voted more for George Bush
the vote variable has three levels.
We need to create a new variable that indicates just whether people voted for or against Bush, because for a T-test to operate we need two groups. Earlier our two groups were the treatment and the control for whether people watched the tv commercials. Here the two groups are wether people voted for Bush or not.
Rather than splitting the vote92 data set into two halves using subset (like we did earlier) we can just use the ~ operator. ~ is a t1lde mark. ~ can be used to define indicate the varaible being tested (persfinance) and the two groups for our analysis (Bush). This is a little quicker than using subset, and we’ll use the tilde mark in future work in the course.
The answer is yes, those who viewed their personal finances as improving were more likely to vote for Bush. The pvalue indicates that the difference in means between the two groups was highly unlikely to have occured by chance. It is not impossible, but it is highly unlikely so we can declare there is a significant difference.
9.4 Populations and samples
Let’s think more about the example we just did. With the the 1992 eletion data, we declared that people with improving personal finances were more likely to vote for Bush. Why do we need test anything about them, we know who they voted for? It’s beause we have a sample of respondents, similar to an exit poll, but what we’re concnered about is all voters. We want to know if people outside the 909 we have data for were more likly to vote for Bush if their personal finances improved. That’s what the test is telling us, that there is a difference in the population (all voters). Just looking at the means between the two groups tells us that there is a difference in our sample. But we rarely care about the sample, what concerns us is projecting or inferring the qualities of others we haven’t asked.
9.5 The problem with .05
That brings us to discuss the .05 test more directly. What would it have meant if the P value had been .06. Well, we would have failed to reject the null. We wouldn’t feel confident enough to say there is a difference in the population. But there would still be a difference in the sample.
Is there a large difference between a P value of .04 and .05 and .06? No, not really. and .05 is a fairly arbitrary standard. Probabilities exist as a continuoum without clear cut offs. A P value of .05 means we’re much more confident than a P value of .6 and a little more confident than a P value of .15. The standard for such a test has to be set somewhere, but we shouldn’t hold .05 as a golden standard.
What does a probability of .05 mean? Let’s think back to the chapter on probability’ it’s equivalent to 1/20. When we set .05 as a standard for hypothesis testing, we’re saying we want to know that there is only a 1 in 20 chance that the difference in voting rates created by the Rock The Vote commercials is by random luck, and to know that 19 out of 20 times it’ll be a true difference between the groups.
So when we get a P value of .05 and reject the null hypothesis, we’re doing so because we think a difference between the two groups is most likely explained by the commercials (or whatever we’re testing). But implicit in a .05 P value is that random chance isn’t impossible, just unlikely. But there is still a 1/20 chance that the difference in voting rates seen after the commercials just occured by random chance and had nothing to do with the commercial. And similarly to flipping a coin, if we do 20 seperate tests in one of them we’ll get a significant value that is generated by random chance. That is a false positive, and we can never identify it.
One approach then is to set a higher standard. We could only reject a null hypothesis if we get a P value of .01 or lower. That would mean only 1 in 100 significant results would be from chance along. Or we could use a standard of .001. That would help to reduce false positives, but not eliminate them still.
.05 has been described as the standard for rejecting the null hypothesis here, but it’s really more of a minimum. Scholars prefer their P values to be .01 or lower when possible, but generally accept .05 as indicative of a significant difference.
9.6 One more problem
Let’s go back to how we calculated P values.
How can we get a larger t-statistic and be more likely to get a significant result? Having a larger difference in the means is one way. That would mean the numerator would get larger. The other way is to make the denomenator smaller, so that whatever the difference in the means is comparatively larger.
If we grow the size of our sample, the n1 and n2, that would shrink the denomenator. That makes intuative sense too. We shouldn’t be very confident if we talk to 10 people and find out that the democrats in the group like cookies more than the republicans. But if we talked to 10 million people, that would be a lot of evidence to disregard if there was a difference in our mean. As we grow our sample size, it becomes more likely that any difference in our means will create a significant finding with a P value of .05 or smaller.
That’s good right? It means we get more precise results, but it creates another concern. When we use larger quantitives of data it becomes necessary to ask whether the differences are significant, as well as large. If I surveyed 10 million voters and found that 72.1 percent of democrats like cookies and only 72.05 republicans like cookies, would the difference be significant?
Yes, that finding is very very significant. Is it meaningful? Not really. There is a statistical difference between the two groups, but that difference is so small it doesn’t help someone to plan a party or pick out deserts. With large enough samples the color of your shirt might impact pay by .13 cents or putting your left shoe on first might add 79 minutes to your life. But those differences lack magnitude to be valuable. Thus, as data sets grow in size it becomes important to test for significance, but also the magnitude of the differences to find what’s meaningfull. Unfortunately, evaluating whether a difference is large is a matter of opinion, and can’t be tested for with certainty.
Those are the basics of hypothesis tests with t-tests. We’ll continue to expand on the tests we can run in the following chapters. Next we’ll talk about a specific instance where we use the tools we’ve discussed: polling.
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