You are currently viewing 20 Uses of the Chi-square Test

20 Uses of the Chi-square Test

The Chi-square test is a commonly used term in research studies. This test is especially useful for those studies involving sampling techniques. It is mainly used for measuring the divergence and difference of the noted frequencies or results in a sample test. However, the Chi-square test also finds application in several other fields, as this article will discuss.

The following outlines 20 major uses of the Chi-square test;


1. Cryptanalysis

In this process, the Chi-square test is used for the comparison of how plaintext and decrypted ciphertext distributes in a chosen sample. The registered lowest value of the Chi-square test indicates that the decryption was a success.

2. Bioinformatics

The Chi-square test in bioinformatics is used for comparing how particular gene properties distribute in different gene category samples. They compared gene properties could be the gene’s content, mutation rate, among other gene properties.

3. The hypothesis of No Association

The Chi-square test is used in the test of the hypothesis of no association. This test could be between sample groups, population, or any other sampling process used. In this test, the recorded cell count is compared to the count which would be expected under the hypothesis.

4. Hypothesis of Association

Similar to the test of the hypothesis of no association, the test of the hypothesis of association is also done using the Chi-square test. The test is usually done in samples of groups or populations exceeding two.

5. Testing the Strength of Association

The strength of the association is a common element in studies such as the cohort study and the cross-sectional study. To test this strength of association, a Chi-square test is used.

6. Medical Literature

In this field, the Chi-square test is mainly used for the comparison of incidences (or, proportions). These incidences are usually of the characteristics of two different groups.

7. Pearson’s Chi-square Test

This is the most common use of the Chi-square test. It is used to make Pearson’s Chi-square test, which is an essential tool used for comparing two or more categories, whose categorical data has been provided.

8. Testing for a Population Variance

The Chi-square test is used to test the variance of two or more population groups. Testing for the variance of a population promotes a better understanding of how and why a population is distributed in a particular manner.

9. Testing for Statistical Independence

Tests for statistical independence are common in contingency tables. The statistical dependency of two variables can be determined using the Chi-square test. An example of such a test is where the Chi-square test is used for determining if the act of smoking causes cancer or not.

10. Testing for Goodness of Fit

As the name suggests, the main purpose of the test for goodness of fit is checking how good a particular sample model is. The Chi-square test is used to test for goodness of fit. An example of a test for goodness of fit, where the Chi-square test is used, is the process of determining how many 6 of dice appear when 3 dices are thrown at the same time, 100 times.

11. Testing for Homogeneity

Take, for example, all the available TV channels, movies, and music. A study may be conducted to determine if and how the distribution of viewing these TV channels compare between the male and female gender. This would be a test for Homogeneity and is usually done using a Chi-square test.

12. The hypothesis of Equal Probability

The Chi-square test is also used to test how the noted results are divergent from the expected results. The base of these expected results is usually the hypothesis of equal probability.

13. The hypothesis of Normal Distribution

Sometimes, the expected results of the sample size can be based on a normal distribution. When this is the case, the Chi-square test is used for comparing the divergence of these recorded results from the expected results.

14. Tests Involving Predetermined Results

The Chi-square test is also used when the expected results are based on predetermined results. Using the Chi-square test, the observed results of a sample table cell are compared with the already predetermined results.

15. Calculation of χ2

In the calculation of χ2, a person is required to make corrections for discontinuity, or Yates’ correction. These corrections can be easily done using the Chi-square test. X2 is used for testing of hypotheses.

16. Market Research

The Chi-square test is an essential tool in market research. This is because the test can be used to determine the ‘goodness of fit’ of an item. Such a test helps in determining whether a particular item in the market has good quality, and hence, it’s potential for selling.

17. Determining Survey Results

In surveying, the Chi-square test is used to analyze the cross-tabulations of the recorded data. The analysis of cross-tabulations is important since it indicates the frequency and percentage of the response data of the conducted survey.

18. Comparing Education and Marriage

All over the world, marriage and education go hand in hand, with each playing a role and affecting the other in a particular way. The Chi-square test can, therefore, be used in the research to find out how many people in a given sample population are affected by education and marriage.

19. Inferential Statistics

Inferential statistics is where data is taken from given smaller samples, then used to make general conclusions about the entire sample. An example of inferential statistics is where, in a mall with 1000 people, only 100 people are interviewed on whether they like shopping in the mall. The data provided by these 100 people are then used to give generalized feedback about the mall. The Chi-square test is used in inferential statistics.

20. Probability of Occurrence

The Chi-square test is used for determining the likelihood of an event happening. This is known as the probability of occurrence. Determining this probability can help a person or an organization to plan their events well.


You may not have a passion for mathematics. However, learning about the many uses that the Chi-square test has, should create in you a passion for learning about this test. Some simple calculations made using the Chi-square test could be the key to the success of your research or business marketing.

Leave a Reply