There are two different tests for applying chi square distribution given in the textbook. The two tests are chi-square goodness-of-fit tests and the chi-square test for independence. The two tests are used differently in the application of chi square distribution.
Chi square, goodness of test fit, a parametric test, is used to determine how the value of a given phenomenon is significantly different from the expected value. The term goodness of test fit is used to compare observed sample distribution with expected probability distribution (Gravetter et al., 2018). The chi square goodness of test fit determines how a theoretical distribution such as Poisson or binomial fits well in the empirical distribution. Also, here, sample data are divided into intervals, and then a comparison is made between the numbers of points that fall into the interval and expected number of points in each interval. In a workplace, chi square goodness of test fit can be used to determine whether the ratio of male and female employees in a department match the overall action of male to female in the company.
On the other hand, the chi-square test for independence is used when there are two categorical variables in a single population and the aim is to determine whether the two variables significantly associate. In the chi square test for independence, simple random sampling is the technique used, the variables are categorical, and the sample data is displayed in a contingency table (Gravetter, et al., 2018). The test has four steps which are stating the hypothesis, formulation of analysis plan, analysis of sample data, and interpretation of the results. For example, in a working place, employees can be classified by gender and their technical abilities. Here, chi square test for independence can be used to determine whether gender is related to technical abilities. In this case, technical abilities refer to ability to work in jobs that require technical skills.
Gravetter, F. J., Wallnau, L. B., & Forzano, L.-A. B. (2018). Essentials of statistics for the behavioral sciences. Boston, MA: Cengage Learning.
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