Module Seven compared several population means through a statistical procedure called analysis of variance (ANOVA). Module Eight introduces contingency tables to summarize categorical data and a chi-square test for the independence of two categorical sets of data.
The previous modules of this course considered data that is quantitative and measurable. This module examines count data that falls into categories, or classes. Count data can be summarized with the use of contingency tables. A contingency table displays counts for two variables measured on a nominal level of measurement. You may recall that nominal data is count data with no natural order to the categories. For example, a business school dean may categorize accounting graduates by gender and whether or not they have passed the certified public accountant (CPA) examinations. That data is summarized in the following contingency table:
|Gender||Passed CPA Exam||Did Not Pass CPA Exam||Total|
Related to contingency tables is the chi-square test of independence for two categorical variables. Consider the following examples:
Hypotheses that accompany a chi-square test of independence include a null hypothesis of independence between two categorical variables and an alternative hypothesis that a relationship exists between the two categorical variables. As Module Eight will show, the chi-square test is useful for establishing the independence of two variables that cannot be quantified and measured, nor analyzed by the traditional correlation coefficient.
You volunteer some of your spare time to your local fire department and have been asked by an assistant chief to analyze data on firefighters who applied for promotion. The assistant chief wants to ensure that gender bias is not a concern in the promotion of firefighters. Shown below is data for 50 firefighters who applied for promotion and the results of a chi-square analysis of the data.
|$15.00||Business, Statistics and Probability||amena||0 time(s)|
|$15.00||no category||DrLoise||0 time(s)|