What is Hypothesis Testing?
Hypothesis testing in statistics refers to analyzing an assumption about a population parameter. It is used to make an educated guess about an assumption using statistics. With the use of sample data, hypothesis testing makes an assumption about how true the assumption is for the entire population from where the sample is being taken.
Any hypothetical statement we make may or may not be valid, and it is then our responsibility to provide evidence for its possibility. To approach any hypothesis, we follow these four simple steps that test its validity.
First, we formulate two hypothetical statements such that only one of them is true. By doing so, we can check the validity of our own hypothesis.
The next step is to formulate the statistical analysis to be followed based upon the data points.
Then we analyze the given data using our methodology.
The final step is to analyze the result and judge whether the null hypothesis will be rejected or is true.
Let’s look at several hypothesis testing examples:
It is observed that the average recovery time for a knee-surgery patient is 8 weeks. A physician believes that after successful knee surgery if the patient goes for physical therapy twice a week rather than thrice a week, the recovery period will be longer. Conduct hypothesis for this statement.
David is a ten-year-old who finishes a 25-yard freestyle in the meantime of 16.43 seconds. David’s father bought goggles for his son, believing that it would help him to reduce his time. He then recorded a total of fifteen 25-yard freestyle for David, and the average time came out to be 16 seconds. Conduct a hypothesis.
A tire company claims their A-segment of tires have a running life of 50,000 miles before they need to be replaced, and previous studies show a standard deviation of 8,000 miles. After surveying a total of 28 tires, the mean run time came to be 46,500 miles with a standard deviation of 9800 miles. Is the claim made by the tire company consistent with the given data? Conduct hypothesis testing.
All of the hypothesis testing examples are from real-life situations, which leads us to believe that hypothesis testing is a very practical topic indeed. It is an integral part of a researcher's study and is used in every research methodology in one way or another.
Inferential statistics majorly deals with hypothesis testing. The research hypothesis states there is a relationship between the independent variable and dependent variable. Whereas the null hypothesis rejects this claim of any relationship between the two, our job as researchers or students is to check whether there is any relation between the two.
Hypothesis Testing in Research Methodology
Now that we are clear about what hypothesis testing is? Let's look at the use of hypothesis testing in research methodology. Hypothesis testing is at the centre of research projects.
What is Hypothesis Testing and Why is it Important in Research Methodology?
Often after formulating research statements, the validity of those statements need to be verified. Hypothesis testing offers a statistical approach to the researcher about the theoretical assumptions he/she made. It can be understood as quantitative results for a qualitative problem.
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Hypothesis testing provides various techniques to test the hypothesis statement depending upon the variable and the data points. It finds its use in almost every field of research while answering statements such as whether this new medicine will work, a new testing method is appropriate, or if the outcomes of a random experiment are probable or not.
Procedure of Hypothesis Testing
To find the validity of any statement, we have to strictly follow the stepwise procedure of hypothesis testing. After stating the initial hypothesis, we have to re-write them in the form of a null and alternate hypothesis. The alternate hypothesis predicts a relationship between the variables, whereas the null hypothesis predicts no relationship between the variables.
After writing them as H0(null hypothesis) and Ha(Alternate hypothesis), only one of the statements can be true. For example, taking the hypothesis that, on average, men are taller than women, we write the statements as:
H0: On average, men are not taller than women.
Ha: On average, men are taller than women.
Our next aim is to collect sample data, what we call sampling, in a way so that we can test our hypothesis. Your data should come from the concerned population for which you want to make a hypothesis.
What is the p value in hypothesis testing? P-value gives us information about the probability of occurrence of results as extreme as observed results.
You will obtain your p-value after choosing the hypothesis testing method, which will be the guiding factor in rejecting the hypothesis. Usually, the p-value cutoff for rejecting the null hypothesis is 0.05. So anything below that, you will reject the null hypothesis.
A low p-value means that the between-group variance is large enough that there is almost no overlapping, and it is unlikely that these came about by chance. A high p-value suggests there is a high within-group variance and low between-group variance, and any difference in the measure is due to chance only.
What is statistical hypothesis testing?
When forming conclusions through research, two sorts of errors are common: A hypothesis must be set and defined in statistics during a statistical survey or research. A statistical hypothesis is what it is called. It is, in fact, a population parameter assumption. However, it is unmistakable that this idea is always proven correct. Hypothesis testing refers to the predetermined formal procedures used by statisticians to determine whether hypotheses should be accepted or rejected. The process of selecting hypotheses for a given probability distribution based on observable data is known as hypothesis testing. Hypothesis testing is a fundamental and crucial issue in statistics.
Why do I Need to Test it? Why not just prove an alternate one?
The quick answer is that you must as a scientist; it is part of the scientific process. Science employs a variety of methods to test or reject theories, ensuring that any new hypothesis is free of errors. One protection to ensure your research is not incorrect is to include both a null and an alternate hypothesis. The scientific community considers not incorporating the null hypothesis in your research to be poor practice. You are almost certainly setting yourself up for failure if you set out to prove another theory without first examining it. At the very least, your experiment will not be considered seriously.
Types of Hypothesis Testing
There are several types of hypothesis testing, and they are used based on the data provided. Depending on the sample size and the data given, we choose among different hypothesis testing methodologies. Here starts the use of hypothesis testing tools in research methodology.
Normality- This type of testing is used for normal distribution in a population sample. If the data points are grouped around the mean, the probability of them being above or below the mean is equally likely. Its shape resembles a bell curve that is equally distributed on either side of the mean.
T-test- This test is used when the sample size in a normally distributed population is comparatively small, and the standard deviation is unknown. Usually, if the sample size drops below 30, we use a T-test to find the confidence intervals of the population.
Chi-Square Test- The Chi-Square test is used to test the population variance against the known or assumed value of the population variance. It is also a better choice to test the goodness of fit of a distribution of data. The two most common Chi-Square tests are the Chi-Square test of independence and the chi-square test of variance.
ANOVA- Analysis of Variance or ANOVA compares the data sets of two different populations or samples. It is similar in its use to the t-test or the Z-test, but it allows us to compare more than two sample means. ANOVA allows us to test the significance between an independent variable and a dependent variable, namely X and Y, respectively.
Z-test- It is a statistical measure to test that the means of two population samples are different when their variance is known. For a Z-test, the population is assumed to be normally distributed. A z-test is better suited in the case of large sample sizes greater than 30. This is due to the central limit theorem that as the sample size increases, the samples are considered to be distributed normally.
FAQs on Hypothesis Testing
1. What is hypothesis testing in statistics?
Hypothesis testing is a formal statistical procedure used to examine an assumption or claim about a population parameter. By analysing sample data, it helps us decide whether there's enough evidence to infer that a particular condition is true for the entire population. It's a method for making decisions under uncertainty.
2. What are the null hypothesis (H₀) and the alternative hypothesis (Hₐ)?
In hypothesis testing, we formulate two competing statements:
- The null hypothesis (H₀) proposes that there is no significant difference, no relationship, or no effect. It represents the status quo or a baseline assumption. For example, H₀: 'The average height of students is 160 cm.'
- The alternative hypothesis (Hₐ or H₁) is the statement that contradicts the null hypothesis. It's what the researcher aims to prove. For example, Hₐ: 'The average height of students is not 160 cm.'
Only one of these hypotheses can be true.
3. What are the main steps to conduct hypothesis testing?
The standard procedure for hypothesis testing involves the following key steps:
- Step 1: State the null (H₀) and alternative (Hₐ) hypotheses clearly.
- Step 2: Choose a significance level (alpha or α), which is the probability of rejecting the null hypothesis when it is true. A common value is 0.05.
- Step 3: Collect sample data and calculate the appropriate test statistic (like a Z-score or t-score).
- Step 4: Determine the p-value, which is the probability of obtaining the observed results if H₀ were true.
- Step 5: Make a decision. If the p-value ≤ α, you reject the null hypothesis. Otherwise, you fail to reject it.
4. What does the p-value tell us in a hypothesis test?
The p-value, or probability value, quantifies the evidence against the null hypothesis. It represents the probability of observing sample data as extreme as, or more extreme than, what was actually collected, assuming the null hypothesis is correct. A small p-value (typically ≤ 0.05) indicates that your observed data is very unlikely under the null hypothesis, providing strong evidence to reject it in favour of the alternative hypothesis.
5. What is the practical difference between a Type I and a Type II error?
Both are potential mistakes in hypothesis testing, but they have different consequences:
- A Type I error is a "false positive." It occurs when you reject a true null hypothesis. For example, concluding a new medicine is effective when it actually has no effect. The probability of this error is denoted by alpha (α).
- A Type II error is a "false negative." It occurs when you fail to reject a false null hypothesis. For example, concluding a new medicine is not effective when it actually is. The probability of this error is denoted by beta (β).
6. How do you decide between using a Z-test and a T-test for testing a mean?
The choice between a Z-test and a T-test depends primarily on the sample size and whether the population standard deviation is known:
- Use a Z-test when the population standard deviation (σ) is known, or when you have a large sample size (typically n > 30), as the sample standard deviation becomes a good estimate of the population standard deviation.
- Use a T-test when the population standard deviation (σ) is unknown and you have a small sample size (typically n < 30).
7. Why is hypothesis testing so crucial for scientific research and data analysis?
Hypothesis testing is crucial because it provides a structured and objective framework for making data-driven decisions. Instead of relying on intuition, it allows researchers to use sample data to draw conclusions about an entire population. It helps to determine if an observed effect is a real phenomenon or simply the result of random chance, which is fundamental for validating scientific theories, testing new treatments, or improving business processes.
