D. The Chi-Square Test

Introduction

One of the most common and useful ways to look at information about the social world is in the format of a table. Say, for example, we want to know whether boys or girls get into trouble more often in school. There are many ways we might show information related to this question, but perhaps the most frequent and easiest to comprehend method is in a table.

  Got in Trouble No Trouble Total
Boys 46 71 117
Girls 37 83 120
Total 83 154 237

The above example is relatively straightforward in that we can fairly quickly tell that more boys than girls got into trouble in school. Calculating percentages, we find that 39 percent of boys got into trouble (46 boys got in trouble out of 117 total boys = 39%), as compared with 31 percent of girls (37 girls got in trouble out of 120 total girls = 31%). However, to re-frame the issue, what if we wanted to test the hypothesis that boys get in trouble more often than girls in school. These figures are a good start to examining that hypothesis; however, the figures in the table are only descriptive. To examine the hypothesis, we need to employ a statistical test, the chi-square test.