**Chi-Square Tests and Examples**

The chi-square goodness of fit test is a parametric trial often used to determine the dissimilarity between the observable and expected values (Tanner, 2016). The chi-square goodness of fit test is applied when using a simple random sampling, where a single qualitative variable exists from one population. The test has four steps: establishing an analytical plan, expressing the hypothesis, and interpreting the findings.

The chi-square goodness of fit test and frequency distribution are similar because they are both used to show different categories, the measures in a dataset with the same characteristics, and the variables (Nihan, 2020). However, they differ because the chi-square goodness of fit test is usually performed in nominal order, whereas the frequency distribution can either be ordered or disordered. Additionally, the numbers in a frequency distribution data set can be seen more than once.

The chi-square test of independence can consist of two variables that can be categorized into several if there are available categories. The variables are usually evaluated to determine if they have a relationship (Nihan, 2020). The fact that both the chi-square test of independence and the chi-square goodness of fit test are conducted in nominal order is what makes them similar. In contrast to the chi-square goodness of fit test, which only employs one variable, the test of independence uses two variables.

Depending on how many variables a certain data set contains, one will decide whether to employ the chi-square test of independence or the chi-square goodness of fit test because a data set with only one variable needs the chi-square goodness of fit test, while a data set with two variables needs the chi-square test of independence.

A real-world example of the chi-square test of independence is when determining the gender of students taking degree courses. The gender of the students consists of two variables: male and female. On the other hand, the degree type consists of several variables. The chi-square test of independence here may be utilized to determine the courses that have more students from a certain gender.

**References**

Nihan, S. T. (2020). Karl Pearson chi-square tests. *Educational Research and Reviews*, *15*(9), 575–580. https://doi.org/10.5897/err2019.3817

Tanner, D. (2016). *Statistics for the Behavioral & Social Sciences* (2nd ed.). Bridgepoint Education.

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**Question**

Prior to beginning work on this discussion forum, read the Instructor Guidance for Week 2; Chapter 10 in the textbook; pages 109 to 120 in Chapter 7 of the Jarman (2013) e-book; the Chi-Square TestLinks to an external site., The Chi-Square Test: Often Used and More Often MisinterpretedLinks to an external site., The Chi-Square Test of IndependenceLinks to an external site., How to Chi-Square TestLinks to an external site., and How to Interpret Chi-SquaredLinks to an external site. articles; watch the Two-Way Tables: Against All Odds – Inside StatisticsLinks to an external site., Chi-Square Tests: Crash Course Statistics #29Links to an external site., Chi-Square Test for Association (Independence) | AP Statistics | Khan AcademyLinks to an external site., and Chi-Square: Lecture 11Links to an external site. Videos.

W2.D.Neighborhood.Group Homes Table.png

Table 10.6 (Tanner, 2016)

The purpose of this discussion is to allow you to consider how nonparametric tests are used and how two types of chi-square tests compare. To do this, you will need to explain statistical concepts and assess assumptions, limitations, and implications associated with statistical tests.

For your initial post,

Describe the chi-square goodness-of-fit test. Explain what this test measures.

Explain how the chi-square goodness-of-fit test is similar to and different from a simple frequency distribution.

Describe the chi-square test of independence. Explain what this test measures and how it is similar to and different from the chi-square goodness-of-fit test.

How do you know when to use one analysis over the other?

Provide a real-world example in which either a goodness-of-fit test or a test of independence should be used.

Guided Response: Review your classmates’ posts and respond to at least two of them. Compare the real-world examples identified by two of your classmates with the one you selected and respond substantively. Do you agree or disagree with their analyses of which test should be used?