Chi-Square Statistical Power and Utility Essay

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Nonparametric Tests

Many interesting questions related to students are categorical. For instance, there is considerable interest in the different enrollment patterns of male and female students in the following majors: Science, technology, engineering, and mathematics (STEM). While the literature does provide robust data for the numbers of students enrolled in these majors, intriguing questions remain that may be better suited to more qualitative data collection. For instance, a research question is: What barriers are perceived by female students with regard to focusing on these majors, and do male students face similar barriers? Categorical representation of presumed barriers could form the basis for a study using Chi-square analysis to explore the frequency of students who identify particular barriers to selecting STEM majors. Chi-square analysis, or goodness of fit, relies on frequency data, which means that it has applicability for nominal data ("SPSS Help Sheet," n.d.).

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The variables of gender and the barrier categories are discrete, categorical (fitting into bins), and nominal ("UCLA Statistics," 2013).

RQ1: What barriers do female and male students perceive with regard to selecting majors in science, technology, engineering, and mathematics (STEM) courses?

H0: there are no differences in the barriers perceived by male and female students with regard to majoring in science, technology, engineering, and mathematics (STEM) courses

H1: there are differences in the barriers perceived by male and female students with regard to majoring in science, technology, engineering, and mathematics (STEM) courses.

The Chi-square test of independence assumes that each subject contributes data to only one cell. This means that the sum of frequencies in the cells of the table must equal the number of subjects in the study (Lane, 2007)......

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