Top Statistical Tests Used in Hypothesis Testing (With Examples)

Are you mathematically faint of heart? Then, conducting research in today’s data-driven world is a hard nut to crack for you. Hypotheses can play a significant role in your decision-making process. But how can you tell if your hypothesis is the right one for your decision?

In that scenario, the statistical tests for hypothesis testing become a beacon of light. Are you curious to know about these tests? This guide will share detailed information about various types of tests that are used for hypothesis testing. Let’s get started.

Major Findings:

In this blog, you will explore:

• Statistical tests help in distinguishing between two sets of data that are used in the research study.
• The key purpose of the statistical testing method is to highlight how two groups are mathematically different from each other.
• The statistical test is divided into two general categories: parametric and non-parametric statistical testing.
• Parametric statistical tests are further sub-categorised into three key types, including regression, comparison, and correlation tests.
• Explore different non-parametric statistical tests with some key examples.
• Learn the key steps that you just follow to choose the right statistical test for hypothesis testing.

Before jumping into different test types, let’s first explore what statistical tests are.

What are Statistical Tests?

The experts of Oxford Brookes University define the statistical test as, “These tests are designed to identify whether two sets of data are mathematically different from each other.” For this identification, these tests use various statistical measures, including the coefficient, mean, standard deviation, and more.

The tests evaluate the two data sets against predefined criteria after calculating these measures. If these sets meet the requirements, then the test concludes that the two sample data sets are mathematically different.

In addition, during this testing, statistical tests make some assumptions, such as:

• No Autocorrelation: The first thing that the statistical test assumes is that the observations or the variables that are included in the test are not related to each other. For instance, it is obvious that multiple variables that are included in a test are not independent, but they are considered independent while conducting a statistical test.
• Homogeneity in Variables: During this testing, it is assumed that the variables in each group being tested are similar across all groups. Because if the entire group has many variations in their variables, then the effectiveness of the test can be impacted.
• Normality of Data: The statistical test is only applicable for data that follows the normal distribution. So, to conduct this test, it is assumed that there is a normal distribution or a bell curve in the data.

Now that you have learned what the statistical test is and what assumptions are required to conduct this test, it’s time to explore different types of this test. Continue reading to get to know these types outlined by the experts at The Academic Papers UK.

Most Important Types of Statistical Tests

Conducting statistical tests is the most common way to analyse two different sets of data. However, analysts use various types of tests depending on the data type sets they are analysing. Knowing the right test is important for successful hypothesis testing. Therefore, we are going to mention some of the most common but important types of this testing.

Check out what these are:

A: Parametric Statistical Tests

According to the experts of the Faculty of Public Health, “The parametric statistical test relies on the data sets that are assumed to be normally distributed.” This type of test requires following precise requirements and strong interference from the data. In addition, researchers collect this type of data only when the given data aligns with common assumptions.

Various types of tests fall into this category. Let’s delve deep into this guide to explore further these test types.

1: Regression Test

The regression test explores the relationship between two or more variables. This means that a change in one or more variables predicts a change in another variable.

It is important to keep in mind that these categorical variables don’t have a causal relationship. We have to test whether one predicts the other or not. It doesn’t mean that one causes the other.

So we can say that "X" predicts "Y", but we can’t ever say that "X" causes "Y". This test is appropriate for usage when you observe the predictive relationship between variables.

In addition, this type of statistical test is further divided into three more categories, including:

• Linear Regression Test: This type of regression test defines the relationship between a dependent and an independent variable using a simple straight line. Generally, it is used for quantitative variables.
• Multiple Regression Test: It is the most common type of regression test in which we study the relationship between one dependent variable and two or more independent variables.
• Logistic Regression Test: The Logistic regression test is usually used for identifying data anomalies that are essential to finding predictive fraud.

Example:

Consider a user can log in to the app using their Gmail account username and password through Google integration. A new feature is being introduced, LinkedIn integration, to log in using your LinkedIn credentials. Now, you can check the new LinkedIn login functionality while tracking the functionality of the previous login method.

2: Comparison Test

Researchers generally base comparison tests on identifying the difference between the mean values of different data sets. Further, it can also be used to analyse the effects of changing the mean value of one data group on the other data group.

Example:

Consider that you want to compare the impacts of two different teaching methods on the students' learning. You have to divide the students into two groups; each group learns from a different method. Then check out their grades. Suppose you collected the following results:

Method A: 76, 82, 90, 77, 65, 79, 70, 92

Method B: 72, 69, 75, 88, 71, 76, 60, 77

To get the average test score, you have to take the mean of the test scores from each group. By comparing the mean values of test scores from both groups, you will find that there is a difference between the mean values of both groups, which will clearly indicate which learning method is better. 

There are various types of this comparison test that we are going to mention below.

• T-Test

The t-test is a statistical test for comparing the means of two groups and identifies whether the two groups are the same or different from each other. During this test, it is assumed that both groups have the same amount of variance.

In short, this test is the right option for hypothesis testing when you compare the different means. Plus, this test is suitable when your sample size is less than 30, and the standard deviation is unknown.

There are various types of these T-tests. Have a look at what these are:

• Paired T-test: This test is the best for comparing the mean values of two variables from the same data groups. It helps you to pick the right sample from the same group.
• Independent T-test: This t-test is also known as the two-sample test. The key purpose of this test is to identify the difference between the mean values of two unrelated groups.
• One-Sample T-test: The one-sample t-test is completely opposite to the independent t-test. In this test, the mean values of two variables from the same group are being compared.

• Z-Test

The Z-test is a way of identifying the differences between two population means when the variance is given. The required sample size of the population for this test is larger than 30. It also follows a normal distribution for hypothesis testing.

Researchers have found that the Z-test and the t-test share many similarities. When it comes to the t-test, the standard deviation is unknown. Whereas the Z-test is right to use when you have a large random sample. The aspect of standard deviation is also provided in its case. Apart from this one shortcoming, the t-test is a better option than the z-test.

• ANOVA

When you have to compare more than two means, ANOVA is a good option. ANOVA separates observed variance data for further tests. It is important to highlight that there are two types of ANOVA, including one-way and two-way ANOVA.

3: Correlation Test

We use a correlation test to observe the relationship between two variables. It doesn’t matter whether the relationship is causal or not. Because these variables have a linear relationship with each other, they change together at the same rate.

Correlation is a common tool for observing the relationship between these variables. For hypothesis testing, you don’t need to make a statement about cause and effect. The key thing that you must consider during this type of test is the Pearson Correlation Coefficient.

This coefficient is used to measure the linear correlation between two variables. The value of this coefficient lies between -1 and 1, which determines the strength and the relationship type between two variables.

Example:

There is a correlation between the heights of parents and their children. This test is best suited for when you want to see the linear relationship between two variables. You don’t have to define cause in your hypothesis either. You only have to observe the relationship in hypothesis testing.

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B: Non-parametric Statistical Tests

In a research study, the non-parametric statistical tests are defined as “They are known as the distribution-free test as they don’t base on testing the normality. These tests are used when assumptions of the parametric tests are not met.”

Generally, the researchers use this type of statistical test when one or more statistical assumptions are violated, and researchers need to verify the data set against some normality criteria. However, these tests are considered less accurate than parametric tests.

Below is a list of some of the most common non-parametric statistical tests:

1: Chi-square Test

The chi-square test is a way of checking the relationship between categorical variables. This test tells about the difference that exists between observed and expected values. The main idea behind the test is to compare observed and expected values if the null hypothesis is true.

Chi-square is best for hypothesis testing when it comes to observing the relationship between categorical variables. It is also the right type of test for identifying the differences between observed and expected values.

Example:

Consider a financial analyst who wants to estimate the extent of the risk that is associated with his investment. For this estimation, rather than using the normal distribution of his earnings, he must use a histogram based on a non-parametric approach to estimate his earnings.

2: Wilcoxon Rank Sum Test

The Wilcoxon rank sum test is also known as the signed rank test, involves working on data sets from paired groups. The key purpose of this group is to compare the data extracted from two paired groups. During this comparison, the researchers evaluate each set of paired groups and identify the difference between them.

Apart from that, this type of non-parametric test is used to compare two related samples, identical samples, and asymmetric samples. Plus, sometimes it happens that you have to repeat measurements on the same sample to identify the population mean. You can analyse the data mean with the help of this test.

Example:

To find a relationship between sleep cycle and the overall health of humans, parametric tests are not the best option, as they can make the process more complicated. So, use the non-parametric approach to analyse the sleep cycle and illness frequency.

3: Mann-Whitney U Test

This test is also known as the Mann-Whitney-Wilcoxon test, which is typically designed for testing the null hypothesis. During this test, you have to select one value from one sample while selecting the other value from the other sample.

There is no requirement to select both sample numbers of the same value; you can pick one sample with a higher value, whereas the other sample has a lower value. The key purpose of this test is to compare the properties of two independent variables with continuous dependent variables.

Example:

The best example of the Mann-Whitney U test is to check the consumer preferences for a specific product. During this test, you can give a questionnaire to various customers of a brand for a specific product and know their preferences about the product.

4: Friedman Test

The Friedman test is similar to the ANOVA test, which is a parametric test. The only thing that distinguishes the Friedman test from the ANOVA test is that the Friedman test is based on repeated measurements, while repeated measurements are not allowed in ANOVA.

The key purpose of this test is to identify the differences between the two variables from the independent groups. One thing you must make sure of is that the dependent variable is from the ordinal spectrum. The best part of this test is that it can be applied to a block design that researchers sometimes call the Durbin method.

Example:

This testing method is best for the social science research project, where you have to handle various nominal variables such as age, qualification, gender, marital status, employment rate, and more. To handle these non-statistical variables, you can use the Friedman test.

How to Choose the Right Statistical Test? 5 Essential Ways

As you have explored various statistical tests for your hypothesis testing, we hope that you have a better understanding of this testing. But knowing the different tests is not enough; the main thing is choosing the right testing method.

You can follow the steps below to select the test method that best suits your needs.

1: Understand the Research Question

A research question is the culmination of the research aims and objectives. When you get a good understanding of this question, you will better know what you want to achieve through your research, which eventually leads you to pick the right statistical test. Thus, we can say that understanding the research question is the foundational step of choosing a good statistical test for hypothesis testing.

2: Decide Between One-tailed and Two-tailed

At this stage, you have to decide whether you have to perform a one-tailed or two-tailed test. If you have clear evidence that your research will go in one direction, then specify the test as one-tailed. On the contrary, if you have no idea about the particular direction of your research, then you must go with the two-tailed test.

3: Specify the Number of Variables

The number of variables plays an important role in the selection of the right statistical test method. The reason behind this importance is that these tests are based on the number of variables that are being analysed. Therefore, identify the number of variables that you are going to analyse in your research.

4: Type of Data

After specifying the number of variables, you have to define whether your data is continuous, binary, or categorical. For instance, if you are handling continuous data, it is obvious that this data is normally distributed, and you have to go with a parametric statistical test.

5: Select the Paired or Unpaired Design

At the end of this selection process, you have to select whether your research design is paired or unpaired. Paired design means that you have to compare two samples that are generally dependent on each other. On the other side, an unpaired study design means two independent variables are being compared. Selecting between these designs will help you narrow down your choices for statistical tests.

Conclusion

A powerful and well-structured hypothesis is the foundation of a successful research study. To make sure that your hypothesis is well-structured, you have to first test it. Statistical tests are the best solution to test these hypotheses. These tests are designed to identify whether two data groups are statistically different from each other.

However, various statistical tests are available out there. Each type of test has unique requirements, study protocols, and procedures. In this guide, we have shared a brief introduction to these tests with an example for your better understanding. We hope that this will help you to better understand them. With this, we also shared some key steps that you must follow to pick the best test that best suits your research needs.

If, after following our guidelines, you are still unsure about picking the right hypothesis testing, ask for dissertation writing help from our UK-based writers. They will not only assist you in choosing the best statistical testing method but also help you in conducting this test successfully.

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