Chi-Square Test for Independence

The chi-square test for independence is a significance test of the relationship between categorical variables. This test is sometimes known as the “Pearson's chi-square” in honor of its developer, Karl Pearson. As an example of this test, consider an experiment by David M. Lane, S. Camille Peres, Aniko Sándor, and H. Al Napier that evaluated the effectiveness of a new method for initiating computer commands. One group of participants was tested using a mouse; a second group was tested using a track pad. Although for both groups, the new method led to faster performance than did the standard method, the question addressed here is whether there was any relationship between preference for the new method and the type of pointing device (mouse or track pad).

Table 1 is a contingency table showing whether preference is contingent on the device used. As can be seen in Table 1, 4 of the 12 participants in the mouse group (33%), compared with 9 of the 10 participants (90%) in the track pad group, preferred the new method. Therefore, in this sample, there is an association between the pointing device used and the method preferred. A key question is whether this association in the sample justifies the conclusion that there is an association in the population.

The chi-square test for independence, as applied to this experiment, tests the null hypothesis that the preferred method (standard or new) is independent of the pointing device used (mouse or track pad). Another way of stating this null hypothesis is that there is no association between the categorical variables of preferred method and pointing device. If the null hypothesis is rejected, then one can conclude that there is an association in the population.