Chi-Square

This chapter introduces students to nonparametric tests, which allow us to draw inferences about nominal or ordinal data. This chapter’s focus is the Chi-Square test, used for analyzing nominal-level data. The Goodness of Fit Χ2 tests an expectation of frequencies, whereas the Χ2 Test of Independence determines to what extent two categories of data differ from each other. These statistics are each discussed in turn, using examples and equations as students are walked step-by-step through the calculations. For the Goodness of Fit Χ2 test, we ask whether a specific course is populated by mostly seniors; the professor expects 75% of her students to be seniors, and we test this expectation. Students learn how to calculate expected frequencies, complete the calculations to arrive at the obtained value of Χ2, and then utilize the statistical table to find the critical value of Χ2 to complete the hypothesis test. For the Goodness of Fit test, Cohen’s ω provides our necessary measure of effect size. Results are presented in APA (seventh edition) formatting. For the Test of Independence, we ask whether two dating websites have similar levels of success. Again, students are walked step-by-step through determining the expected frequencies and computing the obtained value of Χ2. For the Test of Independence, ϕ is utilized to measure effect size; results are then interpreted and presented in APA (seventh edition) format. We then provide brief concluding remarks encouraging students to continue their study of statistics and explore multivariate statistics or additional nonparametric statistics. The chapter concludes with a brief summary, and step-by-step illustrated instructions are provided for helping students utilize Excel to calculate the Chi-Square statistic. Critical thinking questions and practice problems are provided.