Day
Temp
Monday
77
Tuesday
76
Wednesday
74
Thursday
78
Friday
78
This value falls so far into the tail that it cannot even be plotted on the distribution ( Figure 7.7 )! Because the result is significant, you also calculate an effect size:
The effect size you calculate is definitely large, meaning someone has some explaining to do!
Figure 7.7. Obtained z statistic. (“ Obtained z5.77 ” by Judy Schmitt is licensed under CC BY-NC-SA 4.0 .)
You compare your obtained z statistic, z = 5.77, to the critical value, z * = 1.645, and find that z > z *. Therefore you reject the null hypothesis, concluding:
Reject H 0 . Based on 5 observations, the average temperature ( M = 76.6 degrees) is statistically significantly higher than it is supposed to be, and the effect size was large, z = 5.77, p < .05, d = 2.60.
Example C Different Significance Level
Finally, let’s take a look at an example phrased in generic terms, rather than in the context of a specific research question, to see the individual pieces one more time. This time, however, we will use a stricter significance level, a = .01, to test the hypothesis.
We will use 60 as an arbitrary null hypothesis value:
We will assume a two-tailed test:
We have seen the critical values for z tests at a = .05 levels of significance several times. To find the values for a = .01, we will go to the Standard Normal Distribution Table and find the z score cutting off .005 (.01 divided by 2 for a two-tailed test) of the area in the tail, which is z * = ±2.575. Notice that this cutoff is much higher than it was for a = .05. This is because we need much less of the area in the tail, so we need to go very far out to find the cutoff. As a result, this will require a much larger effect or much larger sample size in order to reject the null hypothesis.
We can now calculate our test statistic. We will use s = 10 as our known population standard deviation and the following data to calculate our sample mean:
The average of these scores is M = 60.40. From this we calculate our z statistic as:
The Cohen’s d effect size calculation is:
Our obtained z statistic, z = 0.13, is very small. It is much less than our critical value of 2.575. Thus, this time, we fail to reject the null hypothesis. Our conclusion would look something like:
Fail to reject H 0 . Based on the sample of 10 scores, we cannot conclude that there is an effect causing the mean ( M = 60.40) to be statistically significantly different from 60.00, z = 0.13, p > .01, d = 0.04, and the effect size supports this interpretation.
There are several other considerations we need to keep in mind when performing hypothesis testing.
In the Physicians’ Reactions case study, the probability value associated with the significance test is .0057. Therefore, the null hypothesis was rejected, and it was concluded that physicians intend to spend less time with obese patients. Despite the low probability value, it is possible that the null hypothesis of no true difference between obese and average-weight patients is true and that the large difference between sample means occurred by chance. If this is the case, then the conclusion that physicians intend to spend less time with obese patients is in error. This type of error is called a Type I error. More generally, a Type I error occurs when a significance test results in the rejection of a true null hypothesis.
The second type of error that can be made in significance testing is failing to reject a false null hypothesis. This kind of error is called a Type II error . Unlike a Type I error, a Type II error is not really an error. When a statistical test is not significant, it means that the data do not provide strong evidence that the null hypothesis is false. Lack of significance does not support the conclusion that the null hypothesis is true. Therefore, a researcher should not make the mistake of incorrectly concluding that the null hypothesis is true when a statistical test was not significant. Instead, the researcher should consider the test inconclusive. Contrast this with a Type I error in which the researcher erroneously concludes that the null hypothesis is false when, in fact, it is true.
A Type II error can only occur if the null hypothesis is false. If the null hypothesis is false, then the probability of a Type II error is called b (“beta”). The probability of correctly rejecting a false null hypothesis equals 1 − b and is called statistical power . Power is simply our ability to correctly detect an effect that exists. It is influenced by the size of the effect (larger effects are easier to detect), the significance level we set (making it easier to reject the null makes it easier to detect an effect, but increases the likelihood of a Type I error), and the sample size used (larger samples make it easier to reject the null).
Misconceptions about significance testing are common. This section lists three important ones.
Your answer should include mention of the baseline assumption of no difference between the sample and the population.
Alpha is the significance level. It is the criterion we use when deciding to reject or fail to reject the null hypothesis, corresponding to a given proportion of the area under the normal distribution and a probability of finding extreme scores assuming the null hypothesis is true.
We always calculate an effect size to see if our research is practically meaningful or important. NHST (null hypothesis significance testing) is influenced by sample size but effect size is not; therefore, they provide complimentary information.
“ Null Hypothesis ” by Randall Munroe/xkcd.com is licensed under CC BY-NC 2.5 .)
Introduction to Statistics in the Psychological Sciences Copyright © 2021 by Linda R. Cote Ph.D.; Rupa G. Gordon Ph.D.; Chrislyn E. Randell Ph.D.; Judy Schmitt; and Helena Marvin is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.
Hypothesis testing is as old as the scientific method and is at the heart of the research process.
Research exists to validate or disprove assumptions about various phenomena. The process of validation involves testing and it is in this context that we will explore hypothesis testing.
A hypothesis is a calculated prediction or assumption about a population parameter based on limited evidence. The whole idea behind hypothesis formulation is testing—this means the researcher subjects his or her calculated assumption to a series of evaluations to know whether they are true or false.
Typically, every research starts with a hypothesis—the investigator makes a claim and experiments to prove that this claim is true or false . For instance, if you predict that students who drink milk before class perform better than those who don’t, then this becomes a hypothesis that can be confirmed or refuted using an experiment.
Read: What is Empirical Research Study? [Examples & Method]
1. simple hypothesis.
Also known as a basic hypothesis, a simple hypothesis suggests that an independent variable is responsible for a corresponding dependent variable. In other words, an occurrence of the independent variable inevitably leads to an occurrence of the dependent variable.
Typically, simple hypotheses are considered as generally true, and they establish a causal relationship between two variables.
Examples of Simple Hypothesis
A complex hypothesis is also known as a modal. It accounts for the causal relationship between two independent variables and the resulting dependent variables. This means that the combination of the independent variables leads to the occurrence of the dependent variables .
Examples of Complex Hypotheses
As the name suggests, a null hypothesis is formed when a researcher suspects that there’s no relationship between the variables in an observation. In this case, the purpose of the research is to approve or disapprove this assumption.
Examples of Null Hypothesis
Read: Research Report: Definition, Types + [Writing Guide]
To disapprove a null hypothesis, the researcher has to come up with an opposite assumption—this assumption is known as the alternative hypothesis. This means if the null hypothesis says that A is false, the alternative hypothesis assumes that A is true.
An alternative hypothesis can be directional or non-directional depending on the direction of the difference. A directional alternative hypothesis specifies the direction of the tested relationship, stating that one variable is predicted to be larger or smaller than the null value while a non-directional hypothesis only validates the existence of a difference without stating its direction.
Examples of Alternative Hypotheses
Logical hypotheses are some of the most common types of calculated assumptions in systematic investigations. It is an attempt to use your reasoning to connect different pieces in research and build a theory using little evidence. In this case, the researcher uses any data available to him, to form a plausible assumption that can be tested.
Examples of Logical Hypothesis
After forming a logical hypothesis, the next step is to create an empirical or working hypothesis. At this stage, your logical hypothesis undergoes systematic testing to prove or disprove the assumption. An empirical hypothesis is subject to several variables that can trigger changes and lead to specific outcomes.
Examples of Empirical Testing
When forming a statistical hypothesis, the researcher examines the portion of a population of interest and makes a calculated assumption based on the data from this sample. A statistical hypothesis is most common with systematic investigations involving a large target audience. Here, it’s impossible to collect responses from every member of the population so you have to depend on data from your sample and extrapolate the results to the wider population.
Examples of Statistical Hypothesis
Hypothesis testing is an assessment method that allows researchers to determine the plausibility of a hypothesis. It involves testing an assumption about a specific population parameter to know whether it’s true or false. These population parameters include variance, standard deviation, and median.
Typically, hypothesis testing starts with developing a null hypothesis and then performing several tests that support or reject the null hypothesis. The researcher uses test statistics to compare the association or relationship between two or more variables.
Explore: Research Bias: Definition, Types + Examples
Researchers also use hypothesis testing to calculate the coefficient of variation and determine if the regression relationship and the correlation coefficient are statistically significant.
The basis of hypothesis testing is to examine and analyze the null hypothesis and alternative hypothesis to know which one is the most plausible assumption. Since both assumptions are mutually exclusive, only one can be true. In other words, the occurrence of a null hypothesis destroys the chances of the alternative coming to life, and vice-versa.
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To successfully confirm or refute an assumption, the researcher goes through five (5) stages of hypothesis testing;
Like we mentioned earlier, hypothesis testing starts with creating a null hypothesis which stands as an assumption that a certain statement is false or implausible. For example, the null hypothesis (H0) could suggest that different subgroups in the research population react to a variable in the same way.
Once you know the variables for the null hypothesis, the next step is to determine the alternative hypothesis. The alternative hypothesis counters the null assumption by suggesting the statement or assertion is true. Depending on the purpose of your research, the alternative hypothesis can be one-sided or two-sided.
Using the example we established earlier, the alternative hypothesis may argue that the different sub-groups react differently to the same variable based on several internal and external factors.
Many researchers create a 5% allowance for accepting the value of an alternative hypothesis, even if the value is untrue. This means that there is a 0.05 chance that one would go with the value of the alternative hypothesis, despite the truth of the null hypothesis.
Something to note here is that the smaller the significance level, the greater the burden of proof needed to reject the null hypothesis and support the alternative hypothesis.
Explore: What is Data Interpretation? + [Types, Method & Tools]
Test statistics in hypothesis testing allow you to compare different groups between variables while the p-value accounts for the probability of obtaining sample statistics if your null hypothesis is true. In this case, your test statistics can be the mean, median and similar parameters.
If your p-value is 0.65, for example, then it means that the variable in your hypothesis will happen 65 in100 times by pure chance. Use this formula to determine the p-value for your data:
After conducting a series of tests, you should be able to agree or refute the hypothesis based on feedback and insights from your sample data.
Hypothesis testing isn’t only confined to numbers and calculations; it also has several real-life applications in business, manufacturing, advertising, and medicine.
In a factory or other manufacturing plants, hypothesis testing is an important part of quality and production control before the final products are approved and sent out to the consumer.
During ideation and strategy development, C-level executives use hypothesis testing to evaluate their theories and assumptions before any form of implementation. For example, they could leverage hypothesis testing to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales.
In addition, hypothesis testing is used during clinical trials to prove the efficacy of a drug or new medical method before its approval for widespread human usage.
An employer claims that her workers are of above-average intelligence. She takes a random sample of 20 of them and gets the following results:
Mean IQ Scores: 110
Standard Deviation: 15
Mean Population IQ: 100
Step 1: Using the value of the mean population IQ, we establish the null hypothesis as 100.
Step 2: State that the alternative hypothesis is greater than 100.
Step 3: State the alpha level as 0.05 or 5%
Step 4: Find the rejection region area (given by your alpha level above) from the z-table. An area of .05 is equal to a z-score of 1.645.
Step 5: Calculate the test statistics using this formula
Z = (110–100) ÷ (15÷√20)
10 ÷ 3.35 = 2.99
If the value of the test statistics is higher than the value of the rejection region, then you should reject the null hypothesis. If it is less, then you cannot reject the null.
In this case, 2.99 > 1.645 so we reject the null.
The most significant benefit of hypothesis testing is it allows you to evaluate the strength of your claim or assumption before implementing it in your data set. Also, hypothesis testing is the only valid method to prove that something “is or is not”. Other benefits include:
Several limitations of hypothesis testing can affect the quality of data you get from this process. Some of these limitations include:
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Simple guide on pure or basic research, its methods, characteristics, advantages, and examples in science, medicine, education and psychology
In this article, we will discuss the concept of internal validity, some clear examples, its importance, and how to test it.
This article will discuss the two different types of errors in hypothesis testing and how you can prevent them from occurring in your research
We are going to discuss alternative hypotheses and null hypotheses in this post and how they work in research.
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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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:
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.
Quick tips on writing a hypothesis
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.
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.
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.
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.
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.
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”.
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."
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."
• 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
• 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.
• 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".
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.
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."
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.
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.
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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Edward barroga.
1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.
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.
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.
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
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
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 .
Quantitative research questions | Quantitative research hypotheses |
---|---|
Descriptive research questions | Simple hypothesis |
Comparative research questions | Complex hypothesis |
Relationship research questions | Directional hypothesis |
Non-directional hypothesis | |
Associative hypothesis | |
Causal hypothesis | |
Null hypothesis | |
Alternative hypothesis | |
Working hypothesis | |
Statistical hypothesis | |
Logical hypothesis | |
Hypothesis-testing | |
Qualitative research questions | Qualitative research hypotheses |
Contextual research questions | Hypothesis-generating |
Descriptive research questions | |
Evaluation research questions | |
Explanatory research questions | |
Exploratory research questions | |
Generative research questions | |
Ideological research questions | |
Ethnographic research questions | |
Phenomenological research questions | |
Grounded theory questions | |
Qualitative case study questions |
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 .
Quantitative research questions | |
---|---|
Descriptive research question | |
- Measures responses of subjects to variables | |
- Presents variables to measure, analyze, or assess | |
What is the proportion of resident doctors in the hospital who have mastered ultrasonography (response of subjects to a variable) as a diagnostic technique in their clinical training? | |
Comparative research question | |
- Clarifies difference between one group with outcome variable and another group without outcome variable | |
Is there a difference in the reduction of lung metastasis in osteosarcoma patients who received the vitamin D adjunctive therapy (group with outcome variable) compared with osteosarcoma patients who did not receive the vitamin D adjunctive therapy (group without outcome variable)? | |
- Compares the effects of variables | |
How does the vitamin D analogue 22-Oxacalcitriol (variable 1) mimic the antiproliferative activity of 1,25-Dihydroxyvitamin D (variable 2) in osteosarcoma cells? | |
Relationship research question | |
- Defines trends, association, relationships, or interactions between dependent variable and independent variable | |
Is there a relationship between the number of medical student suicide (dependent variable) and the level of medical student stress (independent variable) in Japan during the first wave of the COVID-19 pandemic? |
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 .
Quantitative research hypotheses | |
---|---|
Simple hypothesis | |
- Predicts relationship between single dependent variable and single independent variable | |
If the dose of the new medication (single independent variable) is high, blood pressure (single dependent variable) is lowered. | |
Complex hypothesis | |
- Foretells relationship between two or more independent and dependent variables | |
The higher the use of anticancer drugs, radiation therapy, and adjunctive agents (3 independent variables), the higher would be the survival rate (1 dependent variable). | |
Directional hypothesis | |
- Identifies study direction based on theory towards particular outcome to clarify relationship between variables | |
Privately funded research projects will have a larger international scope (study direction) than publicly funded research projects. | |
Non-directional hypothesis | |
- Nature of relationship between two variables or exact study direction is not identified | |
- Does not involve a theory | |
Women and men are different in terms of helpfulness. (Exact study direction is not identified) | |
Associative hypothesis | |
- Describes variable interdependency | |
- Change in one variable causes change in another variable | |
A larger number of people vaccinated against COVID-19 in the region (change in independent variable) will reduce the region’s incidence of COVID-19 infection (change in dependent variable). | |
Causal hypothesis | |
- An effect on dependent variable is predicted from manipulation of independent variable | |
A change into a high-fiber diet (independent variable) will reduce the blood sugar level (dependent variable) of the patient. | |
Null hypothesis | |
- A negative statement indicating no relationship or difference between 2 variables | |
There is no significant difference in the severity of pulmonary metastases between the new drug (variable 1) and the current drug (variable 2). | |
Alternative hypothesis | |
- Following a null hypothesis, an alternative hypothesis predicts a relationship between 2 study variables | |
The new drug (variable 1) is better on average in reducing the level of pain from pulmonary metastasis than the current drug (variable 2). | |
Working hypothesis | |
- A hypothesis that is initially accepted for further research to produce a feasible theory | |
Dairy cows fed with concentrates of different formulations will produce different amounts of milk. | |
Statistical hypothesis | |
- Assumption about the value of population parameter or relationship among several population characteristics | |
- Validity tested by a statistical experiment or analysis | |
The mean recovery rate from COVID-19 infection (value of population parameter) is not significantly different between population 1 and population 2. | |
There is a positive correlation between the level of stress at the workplace and the number of suicides (population characteristics) among working people in Japan. | |
Logical hypothesis | |
- Offers or proposes an explanation with limited or no extensive evidence | |
If healthcare workers provide more educational programs about contraception methods, the number of adolescent pregnancies will be less. | |
Hypothesis-testing (Quantitative hypothesis-testing research) | |
- Quantitative research uses deductive reasoning. | |
- This involves the formation of a hypothesis, collection of data in the investigation of the problem, analysis and use of the data from the investigation, and drawing of conclusions to validate or nullify the hypotheses. |
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 research questions | |
---|---|
Contextual research question | |
- Ask the nature of what already exists | |
- Individuals or groups function to further clarify and understand the natural context of real-world problems | |
What are the experiences of nurses working night shifts in healthcare during the COVID-19 pandemic? (natural context of real-world problems) | |
Descriptive research question | |
- Aims to describe a phenomenon | |
What are the different forms of disrespect and abuse (phenomenon) experienced by Tanzanian women when giving birth in healthcare facilities? | |
Evaluation research question | |
- Examines the effectiveness of existing practice or accepted frameworks | |
How effective are decision aids (effectiveness of existing practice) in helping decide whether to give birth at home or in a healthcare facility? | |
Explanatory research question | |
- Clarifies a previously studied phenomenon and explains why it occurs | |
Why is there an increase in teenage pregnancy (phenomenon) in Tanzania? | |
Exploratory research question | |
- Explores areas that have not been fully investigated to have a deeper understanding of the research problem | |
What factors affect the mental health of medical students (areas that have not yet been fully investigated) during the COVID-19 pandemic? | |
Generative research question | |
- Develops an in-depth understanding of people’s behavior by asking ‘how would’ or ‘what if’ to identify problems and find solutions | |
How would the extensive research experience of the behavior of new staff impact the success of the novel drug initiative? | |
Ideological research question | |
- Aims to advance specific ideas or ideologies of a position | |
Are Japanese nurses who volunteer in remote African hospitals able to promote humanized care of patients (specific ideas or ideologies) in the areas of safe patient environment, respect of patient privacy, and provision of accurate information related to health and care? | |
Ethnographic research question | |
- Clarifies peoples’ nature, activities, their interactions, and the outcomes of their actions in specific settings | |
What are the demographic characteristics, rehabilitative treatments, community interactions, and disease outcomes (nature, activities, their interactions, and the outcomes) of people in China who are suffering from pneumoconiosis? | |
Phenomenological research question | |
- Knows more about the phenomena that have impacted an individual | |
What are the lived experiences of parents who have been living with and caring for children with a diagnosis of autism? (phenomena that have impacted an individual) | |
Grounded theory question | |
- Focuses on social processes asking about what happens and how people interact, or uncovering social relationships and behaviors of groups | |
What are the problems that pregnant adolescents face in terms of social and cultural norms (social processes), and how can these be addressed? | |
Qualitative case study question | |
- Assesses a phenomenon using different sources of data to answer “why” and “how” questions | |
- Considers how the phenomenon is influenced by its contextual situation. | |
How does quitting work and assuming the role of a full-time mother (phenomenon assessed) change the lives of women in Japan? |
Qualitative research hypotheses | |
---|---|
Hypothesis-generating (Qualitative hypothesis-generating research) | |
- Qualitative research uses inductive reasoning. | |
- This involves data collection from study participants or the literature regarding a phenomenon of interest, using the collected data to develop a formal hypothesis, and using the formal hypothesis as a framework for testing the hypothesis. | |
- Qualitative exploratory studies explore areas deeper, clarifying subjective experience and allowing formulation of a formal hypothesis potentially testable in a future quantitative approach. |
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 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
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.
Variables | Unclear and weak statement (Statement 1) | Clear and good statement (Statement 2) | Points to avoid |
---|---|---|---|
Research question | Which is more effective between smoke moxibustion and smokeless moxibustion? | “Moreover, regarding smoke moxibustion versus smokeless moxibustion, it remains unclear which is more effective, safe, and acceptable to pregnant women, and whether there is any difference in the amount of heat generated.” | 1) Vague and unfocused questions |
2) Closed questions simply answerable by yes or no | |||
3) Questions requiring a simple choice | |||
Hypothesis | The smoke moxibustion group will have higher cephalic presentation. | “Hypothesis 1. The smoke moxibustion stick group (SM group) and smokeless moxibustion stick group (-SLM group) will have higher rates of cephalic presentation after treatment than the control group. | 1) Unverifiable hypotheses |
Hypothesis 2. The SM group and SLM group will have higher rates of cephalic presentation at birth than the control group. | 2) Incompletely stated groups of comparison | ||
Hypothesis 3. There will be no significant differences in the well-being of the mother and child among the three groups in terms of the following outcomes: premature birth, premature rupture of membranes (PROM) at < 37 weeks, Apgar score < 7 at 5 min, umbilical cord blood pH < 7.1, admission to neonatal intensive care unit (NICU), and intrauterine fetal death.” | 3) Insufficiently described variables or outcomes | ||
Research objective | To determine which is more effective between smoke moxibustion and smokeless moxibustion. | “The specific aims of this pilot study were (a) to compare the effects of smoke moxibustion and smokeless moxibustion treatments with the control group as a possible supplement to ECV for converting breech presentation to cephalic presentation and increasing adherence to the newly obtained cephalic position, and (b) to assess the effects of these treatments on the well-being of the mother and child.” | 1) Poor understanding of the research question and hypotheses |
2) Insufficient description of population, variables, or study outcomes |
a These statements were composed for comparison and illustrative purposes only.
b These statements are direct quotes from Higashihara and Horiuchi. 16
Variables | Unclear and weak statement (Statement 1) | Clear and good statement (Statement 2) | Points to avoid |
---|---|---|---|
Research question | Does disrespect and abuse (D&A) occur in childbirth in Tanzania? | How does disrespect and abuse (D&A) occur and what are the types of physical and psychological abuses observed in midwives’ actual care during facility-based childbirth in urban Tanzania? | 1) Ambiguous or oversimplistic questions |
2) Questions unverifiable by data collection and analysis | |||
Hypothesis | Disrespect and abuse (D&A) occur in childbirth in Tanzania. | Hypothesis 1: Several types of physical and psychological abuse by midwives in actual care occur during facility-based childbirth in urban Tanzania. | 1) Statements simply expressing facts |
Hypothesis 2: Weak nursing and midwifery management contribute to the D&A of women during facility-based childbirth in urban Tanzania. | 2) Insufficiently described concepts or variables | ||
Research objective | To describe disrespect and abuse (D&A) in childbirth in Tanzania. | “This study aimed to describe from actual observations the respectful and disrespectful care received by women from midwives during their labor period in two hospitals in urban Tanzania.” | 1) Statements unrelated to the research question and hypotheses |
2) Unattainable or unexplorable objectives |
a This statement is a direct quote from Shimoda et al. 17
The other statements were composed for comparison and illustrative purposes only.
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.
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:
The bottom line.
Hypothesis testing, sometimes called significance testing, is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.
Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population or a data-generating process. The word "population" will be used for both of these cases in the following descriptions.
In hypothesis testing, an analyst tests a statistical sample, intending to provide evidence on the plausibility of the null hypothesis. Statistical analysts measure and examine a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis.
The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis. Thus, they are mutually exclusive , and only one can be true. However, one of the two hypotheses will always be true.
The null hypothesis is a statement about a population parameter, such as the population mean, that is assumed to be true.
If an individual wants to test that a penny has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct, and the alternative hypothesis would be that 50% is not correct. Mathematically, the null hypothesis is represented as Ho: P = 0.5. The alternative hypothesis is shown as "Ha" and is identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.
A random sample of 100 coin flips is taken, and the null hypothesis is tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing on heads and would reject the null hypothesis and accept the alternative hypothesis.
If there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. In cases such as this where the null hypothesis is "accepted," the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is "explainable by chance alone."
Some statisticians attribute the first hypothesis tests to satirical writer John Arbuthnot in 1710, who studied male and female births in England after observing that in nearly every year, male births exceeded female births by a slight proportion. Arbuthnot calculated that the probability of this happening by chance was small, and therefore it was due to “divine providence.”
Hypothesis testing helps assess the accuracy of new ideas or theories by testing them against data. This allows researchers to determine whether the evidence supports their hypothesis, helping to avoid false claims and conclusions. Hypothesis testing also provides a framework for decision-making based on data rather than personal opinions or biases. By relying on statistical analysis, hypothesis testing helps to reduce the effects of chance and confounding variables, providing a robust framework for making informed conclusions.
Hypothesis testing relies exclusively on data and doesn’t provide a comprehensive understanding of the subject being studied. Additionally, the accuracy of the results depends on the quality of the available data and the statistical methods used. Inaccurate data or inappropriate hypothesis formulation may lead to incorrect conclusions or failed tests. Hypothesis testing can also lead to errors, such as analysts either accepting or rejecting a null hypothesis when they shouldn’t have. These errors may result in false conclusions or missed opportunities to identify significant patterns or relationships in the data.
Hypothesis testing refers to a statistical process that helps researchers determine the reliability of a study. By using a well-formulated hypothesis and set of statistical tests, individuals or businesses can make inferences about the population that they are studying and draw conclusions based on the data presented. All hypothesis testing methods have the same four-step process, which includes stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.
Sage. " Introduction to Hypothesis Testing ," Page 4.
Elder Research. " Who Invented the Null Hypothesis? "
Formplus. " Hypothesis Testing: Definition, Uses, Limitations and Examples ."
When interpreting research findings, researchers need to assess whether these findings may have occurred by chance. Hypothesis testing is a systematic procedure for deciding whether the results of a research study support a particular theory which applies to a population.
Hypothesis testing uses sample data to evaluate a hypothesis about a population . A hypothesis test assesses how unusual the result is, whether it is reasonable chance variation or whether the result is too extreme to be considered chance variation.
Effect size and statistical significance.
To carry out statistical hypothesis testing, research and null hypothesis are employed:
H A: There is a relationship between intelligence and academic results.
H A: First year university students obtain higher grades after an intensive Statistics course.
H A; Males and females differ in their levels of stress.
H o : There is no relationship between intelligence and academic results.
H o: First year university students do not obtain higher grades after an intensive Statistics course.
H o : Males and females will not differ in their levels of stress.
The purpose of hypothesis testing is to test whether the null hypothesis (there is no difference, no effect) can be rejected or approved. If the null hypothesis is rejected, then the research hypothesis can be accepted. If the null hypothesis is accepted, then the research hypothesis is rejected.
In hypothesis testing, a value is set to assess whether the null hypothesis is accepted or rejected and whether the result is statistically significant:
The probability value, or p value , is the probability of an outcome or research result given the hypothesis. Usually, the probability value is set at 0.05: the null hypothesis will be rejected if the probability value of the statistical test is less than 0.05. There are two types of errors associated to hypothesis testing:
These situations are known as Type I and Type II errors:
These errors cannot be eliminated; they can be minimised, but minimising one type of error will increase the probability of committing the other type.
The probability of making a Type I error depends on the criterion that is used to accept or reject the null hypothesis: the p value or alpha level . The alpha is set by the researcher, usually at .05, and is the chance the researcher is willing to take and still claim the significance of the statistical test.). Choosing a smaller alpha level will decrease the likelihood of committing Type I error.
For example, p<0.05 indicates that there are 5 chances in 100 that the difference observed was really due to sampling error – that 5% of the time a Type I error will occur or that there is a 5% chance that the opposite of the null hypothesis is actually true.
With a p<0.01, there will be 1 chance in 100 that the difference observed was really due to sampling error – 1% of the time a Type I error will occur.
The p level is specified before analysing the data. If the data analysis results in a probability value below the α (alpha) level, then the null hypothesis is rejected; if it is not, then the null hypothesis is not rejected.
When the null hypothesis is rejected, the effect is said to be statistically significant. However, statistical significance does not mean that the effect is important.
A result can be statistically significant, but the effect size may be small. Finding that an effect is significant does not provide information about how large or important the effect is. In fact, a small effect can be statistically significant if the sample size is large enough.
Information about the effect size, or magnitude of the result, is given by the statistical test. For example, the strength of the correlation between two variables is given by the coefficient of correlation, which varies from 0 to 1.
The hypothesis testing process can be divided into five steps:
This example illustrates how these five steps can be applied to text a hypothesis:
Step 1 : There are two populations of interest.
Population 1: People who go through the experimental procedure (drink coffee).
Population 2: People who do not go through the experimental procedure (drink water).
Step 2 : We know that the characteristics of the comparison distribution (student population) are:
Population M = 19, Population SD= 4, normally distributed. These are the mean and standard deviation of the distribution of scores on the memory test for the general student population.
Step 3 : For a two-tailed test (the direction of the effect is not specified) at the 5% level (25% at each tail), the cut off sample scores are +1.96 and -1.99.
Step 4 : Your sample score of 27 needs to be converted into a Z value. To calculate Z = (27-19)/4= 2 ( check the Converting into Z scores section if you need to review how to do this process)
Step 5 : A ‘Z’ score of 2 is more extreme than the cut off Z of +1.96 (see figure above). The result is significant and, thus, the null hypothesis is rejected.
You can find more examples here:
Correlation analysis, multiple regression.
Correlation analysis explores the association between variables . The purpose of correlational analysis is to discover whether there is a relationship between variables, which is unlikely to occur by sampling error. The null hypothesis is that there is no relationship between the two variables. Correlation analysis provides information about:
A positive correlation indicates that high scores on one variable are associated with high scores on the other variable; low scores on one variable are associated with low scores on the second variable . For instance, in the figure below, higher scores on negative affect are associated with higher scores on perceived stress
A negative correlation indicates that high scores on one variable are associated with low scores on the other variable. The graph shows that a person who scores high on perceived stress will probably score low on mastery. The slope of the graph is downwards- as it moves to the right. In the figure below, higher scores on mastery are associated with lower scores on perceived stress.
Fig 2. Negative correlation between two variables. Adapted from Pallant, J. (2013). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (5th ed.). Sydney, Melbourne, Auckland, London: Allen & Unwin
2. The strength or magnitude of the relationship
The strength of a linear relationship between two variables is measured by a statistic known as the correlation coefficient , which varies from 0 to -1, and from 0 to +1. There are several correlation coefficients; the most widely used are Pearson’s r and Spearman’s rho. The strength of the relationship is interpreted as follows:
It is important to note that correlation analysis does not imply causality. Correlation is used to explore the association between variables, however, it does not indicate that one variable causes the other. The correlation between two variables could be due to the fact that a third variable is affecting the two variables.
Multiple regression is an extension of correlation analysis. Multiple regression is used to explore the relationship between one dependent variable and a number of independent variables or predictors . The purpose of a multiple regression model is to predict values of a dependent variable based on the values of the independent variables or predictors. For example, a researcher may be interested in predicting students’ academic success (e.g. grades) based on a number of predictors, for example, hours spent studying, satisfaction with studies, relationships with peers and lecturers.
A multiple regression model can be conducted using statistical software (e.g. SPSS). The software will test the significance of the model (i.e. does the model significantly predicts scores on the dependent variable using the independent variables introduced in the model?), how much of the variance in the dependent variable is explained by the model, and the individual contribution of each independent variable.
Example of multiple regression model
From Dunn et al. (2014). Influence of academic self-regulation, critical thinking, and age on online graduate students' academic help-seeking.
In this model, help-seeking is the dependent variable; there are three independent variables or predictors. The coefficients show the direction (positive or negative) and magnitude of the relationship between each predictor and the dependent variable. The model was statistically significant and predicted 13.5% of the variance in help-seeking.
t-Tests are employed to compare the mean score on some continuous variable for two groups . The null hypothesis to be tested is there are no differences between the two groups (e.g. anxiety scores for males and females are not different).
If the significance value of the t-test is equal or less than .05, there is a significant difference in the mean scores on the variable of interest for each of the two groups. If the value is above .05, there is no significant difference between the groups.
t-Tests can be employed to compare the mean scores of two different groups (independent-samples t-test ) or to compare the same group of people on two different occasions ( paired-samples t-test) .
In addition to assessing whether the difference between the two groups is statistically significant, it is important to consider the effect size or magnitude of the difference between the groups. The effect size is given by partial eta squared (proportion of variance of the dependent variable that is explained by the independent variable) and Cohen’s d (difference between groups in terms of standard deviation units).
In this example, an independent samples t-test was conducted to assess whether males and females differ in their perceived anxiety levels. The significance of the test is .004. Since this value is less than .05, we can conclude that there is a statistically significant difference between males and females in their perceived anxiety levels.
Whilst t-tests compare the mean score on one variable for two groups, analysis of variance is used to test more than two groups . Following the previous example, analysis of variance would be employed to test whether there are differences in anxiety scores for students from different disciplines.
Analysis of variance compare the variance (variability in scores) between the different groups (believed to be due to the independent variable) with the variability within each group (believed to be due to chance). An F ratio is calculated; a large F ratio indicates that there is more variability between the groups (caused by the independent variable) than there is within each group (error term). A significant F test indicates that we can reject the null hypothesis; i.e. that there is no difference between the groups.
Again, effect size statistics such as Cohen’s d and eta squared are employed to assess the magnitude of the differences between groups.
In this example, we examined differences in perceived anxiety between students from different disciplines. The results of the Anova Test show that the significance level is .005. Since this value is below .05, we can conclude that there are statistically significant differences between students from different disciplines in their perceived anxiety levels.
Chi-square test for independence is used to explore the relationship between two categorical variables. Each variable can have two or more categories.
For example, a researcher can use a Chi-square test for independence to assess the relationship between study disciplines (e.g. Psychology, Business, Education,…) and help-seeking behaviour (Yes/No). The test compares the observed frequencies of cases with the values that would be expected if there was no association between the two variables of interest. A statistically significant Chi-square test indicates that the two variables are associated (e.g. Psychology students are more likely to seek help than Business students). The effect size is assessed using effect size statistics: Phi and Cramer’s V .
In this example, a Chi-square test was conducted to assess whether males and females differ in their help-seeking behaviour (Yes/No). The crosstabulation table shows the percentage of males of females who sought/didn't seek help. The table 'Chi square tests' shows the significance of the test (Pearson Chi square asymp sig: .482). Since this value is above .05, we conclude that there is no statistically significant difference between males and females in their help-seeking behaviour.
Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.
A hypothesis is an assumption or idea, specifically a statistical claim about an unknown population parameter. For example, a judge assumes a person is innocent and verifies this by reviewing evidence and hearing testimony before reaching a verdict.
Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.
To test the validity of the claim or assumption about the population parameter:
Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.
Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing.
One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.
There are two types of one-tailed test:
A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.
Example: H 0 : [Tex]\mu = [/Tex] 50 and H 1 : [Tex]\mu \neq 50 [/Tex]
To delve deeper into differences into both types of test: Refer to link
In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.
Null Hypothesis is True | Null Hypothesis is False | |
---|---|---|
Null Hypothesis is True (Accept) | Correct Decision | Type II Error (False Negative) |
Alternative Hypothesis is True (Reject) | Type I Error (False Positive) | Correct Decision |
Step 1: define null and alternative hypothesis.
State the null hypothesis ( [Tex]H_0 [/Tex] ), representing no effect, and the alternative hypothesis ( [Tex]H_1 [/Tex] ), suggesting an effect or difference.
We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.
Select a significance level ( [Tex]\alpha [/Tex] ), typically 0.05, to determine the threshold for rejecting the null hypothesis. It provides validity to our hypothesis test, ensuring that we have sufficient data to back up our claims. Usually, we determine our significance level beforehand of the test. The p-value is the criterion used to calculate our significance value.
Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.
The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.
There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.
We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.
T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.
In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.
Comparing the test statistic and tabulated critical value we have,
Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.
We can also come to an conclusion using the p-value,
Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.
At last, we can conclude our experiment using method A or B.
To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .
When population means and standard deviations are known.
[Tex]z = \frac{\bar{x} – \mu}{\frac{\sigma}{\sqrt{n}}}[/Tex]
T test is used when n<30,
t-statistic calculation is given by:
[Tex]t=\frac{x̄-μ}{s/\sqrt{n}} [/Tex]
Chi-Square Test for Independence categorical Data (Non-normally distributed) using:
[Tex]\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}[/Tex]
Let’s examine hypothesis testing using two real life situations,
Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.
Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.
If the evidence suggests less than a 5% chance of observing the results due to random variation.
Using paired T-test analyze the data to obtain a test statistic and a p-value.
The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.
t = m/(s/√n)
then, m= -3.9, s= 1.8 and n= 10
we, calculate the , T-statistic = -9 based on the formula for paired t test
The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.
thus, p-value = 8.538051223166285e-06
Step 5: Result
Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.
Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.
Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.
We will implement our first real life problem via python,
import numpy as np from scipy import stats # Data before_treatment = np . array ([ 120 , 122 , 118 , 130 , 125 , 128 , 115 , 121 , 123 , 119 ]) after_treatment = np . array ([ 115 , 120 , 112 , 128 , 122 , 125 , 110 , 117 , 119 , 114 ]) # Step 1: Null and Alternate Hypotheses # Null Hypothesis: The new drug has no effect on blood pressure. # Alternate Hypothesis: The new drug has an effect on blood pressure. null_hypothesis = "The new drug has no effect on blood pressure." alternate_hypothesis = "The new drug has an effect on blood pressure." # Step 2: Significance Level alpha = 0.05 # Step 3: Paired T-test t_statistic , p_value = stats . ttest_rel ( after_treatment , before_treatment ) # Step 4: Calculate T-statistic manually m = np . mean ( after_treatment - before_treatment ) s = np . std ( after_treatment - before_treatment , ddof = 1 ) # using ddof=1 for sample standard deviation n = len ( before_treatment ) t_statistic_manual = m / ( s / np . sqrt ( n )) # Step 5: Decision if p_value <= alpha : decision = "Reject" else : decision = "Fail to reject" # Conclusion if decision == "Reject" : conclusion = "There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different." else : conclusion = "There is insufficient evidence to claim a significant difference in average blood pressure before and after treatment with the new drug." # Display results print ( "T-statistic (from scipy):" , t_statistic ) print ( "P-value (from scipy):" , p_value ) print ( "T-statistic (calculated manually):" , t_statistic_manual ) print ( f "Decision: { decision } the null hypothesis at alpha= { alpha } ." ) print ( "Conclusion:" , conclusion )
T-statistic (from scipy): -9.0 P-value (from scipy): 8.538051223166285e-06 T-statistic (calculated manually): -9.0 Decision: Reject the null hypothesis at alpha=0.05. Conclusion: There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.
In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05.
Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.
Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.
Populations Mean = 200
Population Standard Deviation (σ): 5 mg/dL(given for this problem)
As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.
The test statistic is calculated by using the z formula Z = [Tex](203.8 – 200) / (5 \div \sqrt{25}) [/Tex] and we get accordingly , Z =2.039999999999992.
Step 4: Result
Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL
import scipy.stats as stats import math import numpy as np # Given data sample_data = np . array ( [ 205 , 198 , 210 , 190 , 215 , 205 , 200 , 192 , 198 , 205 , 198 , 202 , 208 , 200 , 205 , 198 , 205 , 210 , 192 , 205 , 198 , 205 , 210 , 192 , 205 ]) population_std_dev = 5 population_mean = 200 sample_size = len ( sample_data ) # Step 1: Define the Hypotheses # Null Hypothesis (H0): The average cholesterol level in a population is 200 mg/dL. # Alternate Hypothesis (H1): The average cholesterol level in a population is different from 200 mg/dL. # Step 2: Define the Significance Level alpha = 0.05 # Two-tailed test # Critical values for a significance level of 0.05 (two-tailed) critical_value_left = stats . norm . ppf ( alpha / 2 ) critical_value_right = - critical_value_left # Step 3: Compute the test statistic sample_mean = sample_data . mean () z_score = ( sample_mean - population_mean ) / \ ( population_std_dev / math . sqrt ( sample_size )) # Step 4: Result # Check if the absolute value of the test statistic is greater than the critical values if abs ( z_score ) > max ( abs ( critical_value_left ), abs ( critical_value_right )): print ( "Reject the null hypothesis." ) print ( "There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL." ) else : print ( "Fail to reject the null hypothesis." ) print ( "There is not enough evidence to conclude that the average cholesterol level in the population is different from 200 mg/dL." )
Reject the null hypothesis. There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL.
Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.
1. what are the 3 types of hypothesis test.
There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.
Null Hypothesis ( [Tex]H_o [/Tex] ): No effect or difference exists. Alternative Hypothesis ( [Tex]H_1 [/Tex] ): An effect or difference exists. Significance Level ( [Tex]\alpha [/Tex] ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.
Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.
Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.
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Step 5: Present your findings. The results of hypothesis testing will be presented in the results and discussion sections of your research paper, dissertation or thesis.. In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p-value).
Formulate the Hypotheses: Write your research hypotheses as a null hypothesis (H 0) and an alternative hypothesis (H A).; Data Collection: Gather data specifically aimed at testing the hypothesis.; Conduct A Test: Use a suitable statistical test to analyze your data.; Make a Decision: Based on the statistical test results, decide whether to reject the null hypothesis or fail to reject it.
Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an ...
HYPOTHESIS TESTING. A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the "alternate" hypothesis, and the opposite ...
Step 1: State the Null Hypothesis. The null hypothesis can be thought of as the opposite of the "guess" the researchers made: in this example, the biologist thinks the plant height will be different for the fertilizers. So the null would be that there will be no difference among the groups of plants. Specifically, in more statistical language ...
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.
This is the basic structure of testing a hypothesis, usually called a hypothesis test. Since this one has a test statistic involving z, it is also called a z-test. And since there is only one sample, it is usually called a one-sample z-test. ... Based on research data, the claim is made that from the time shoots are planted 90 days on average ...
Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables. This post provides an overview of statistical hypothesis testing.
In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis.The null hypothesis is usually denoted \(H_0\) while the alternative hypothesis is usually denoted \(H_1\). An hypothesis test is a statistical decision; the conclusion will either be to reject the null hypothesis in favor ...
8.2 FOUR STEPS TO HYPOTHESIS TESTING The goal of hypothesis testing is to determine the likelihood that a population parameter, such as the mean, is likely to be true. In this section, we describe the four steps of hypothesis testing that were briefly introduced in Section 8.1: Step 1: State the hypotheses. Step 2: Set the criteria for a decision.
This chapter lays out the basic logic and process of hypothesis testing. We will perform z tests, which use the z score formula from Chapter 6 and data from a sample mean to make an inference about a population.. Logic and Purpose of Hypothesis Testing. A hypothesis is a prediction that is tested in a research study. The statistician R. A. Fisher explained the concept of hypothesis testing ...
Applications of Hypothesis Testing in Research. Hypothesis testing isn't only confined to numbers and calculations; it also has several real-life applications in business, manufacturing, advertising, and medicine. ... Simple guide on pure or basic research, its methods, characteristics, advantages, and examples in science, medicine, education ...
Medical providers often rely on evidence-based medicine to guide decision-making in practice. Often a research hypothesis is tested with results provided, typically with p values, confidence intervals, or both. Additionally, statistical or research significance is estimated or determined by the investigators. Unfortunately, healthcare providers may have different comfort levels in interpreting ...
A hypothesis test consists of five steps: 1. State the hypotheses. State the null and alternative hypotheses. These two hypotheses need to be mutually exclusive, so if one is true then the other must be false. 2. Determine a significance level to use for the hypothesis. Decide on a significance level.
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.
A hypothesis test allows us to test the claim about the population and find out how likely it is to be true. The hypothesis test consists of several components; two statements, the null hypothesis and the alternative hypothesis, the test statistic and the critical value, which in turn give us the P-value and the rejection region ...
Components of a Formal Hypothesis Test. The null hypothesis is a statement about the value of a population parameter, such as the population mean (µ) or the population proportion (p).It contains the condition of equality and is denoted as H 0 (H-naught).. H 0: µ = 157 or H0 : p = 0.37. The alternative hypothesis is the claim to be tested, the opposite of the null hypothesis.
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 ...
4 Step Process. State the hypotheses. Formulate an analysis plan, which outlines how the data will be evaluated. Carry out the plan and analyze the sample data. Analyze the results and either ...
Step 4: Your sample score of 27 needs to be converted into a Z value. To calculate Z = (27-19)/4= 2 (check the if you need to review how to do this process) Step 5: A 'Z' score of 2 is more extreme than the cut off Z of +1.96 (see figure above). The result is significant and, thus, the null hypothesis is rejected. You can find more examples ...
148. 4. Photo by Anna Nekrashevich from Pexels. Hypothesis testing is a common statistical tool used in research and data science to support the certainty of findings. The aim of testing is to answer how probable an apparent effect is detected by chance given a random data sample. This article provides a detailed explanation of the key concepts ...
This page titled 1.4: Basic Concepts of Hypothesis Testing is shared under a not declared license and was authored, remixed, and/or curated by John H. McDonald via source content that was edited to the style and standards of the LibreTexts platform. The technique used by the vast majority of biologists, and the technique that most of this ...
Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. ... it is a basic assumption or made based on the problem knowledge. Example: A company's mean production is 50 units ... The Lottery Ticket Hypothesis has been presented in the form of a research paper at ICLR 2019 by MIT-IBM ...
Quantitative research involves the collection and analysis of numerical data to test hypotheses and identify patterns and relationships (Hair et al., Citation 2019). Using a quantitative approach, this study aimed to systematically examine the relationship between green supply chain practices and commercial performance metrics.
The Null hypothesis \(\left(H_{O}\right)\) is a statement about the comparisons, e.g., between a sample statistic and the population, or between two treatment groups. The former is referred to as a one-tailed test whereas the latter is called a two-tailed test. The null hypothesis is typically "no statistical difference" between the ...
We can calibrate the Bayesian probability to the frequentist p-value (Selke et al 2001; Goodman 2008; Held 2010; Greenland and Poole 2012). Methods to achieve this calibration vary, but the Fagan nomogram proposed by Held (2010) is a good tool for us as we go forward. We can calculate our NHST p-value, but then convert the p-value to a Bayes factor by looking at the nomogram.