Significance Testing for Crosstabulations

The purpose of a crosstabulation is to show the relationship (or lack thereof) between two variables. Although there appears to be some relationship between the two variables, is there any reason to believe that the differences in PDA ownership between different income categories is anything more than random variation?

A number of tests are available to determine if the relationship between two crosstabulated variables is significant. One of the more common tests is chi-square. One of the advantages of chi-square is that it is appropriate for almost any kind of data.

  1. Open the Crosstabs dialog box again.
  2. Click Statistics.
    Figure 1. Crosstabs dialog box
    Crosstabs dialog box with row and column variables selected
    Figure 2. Crosstabs Statistics dialog box
    Crosstabs Statistics dialog box
  3. Click (check) Chi-square.
  4. Click Continue and then click OK in the main dialog box to run the procedure.
Figure 3. Chi-square statistics
Chi-square statistics

Pearson chi-square tests the hypothesis that the row and column variables are independent. The actual value of the statistic isn't very informative. The significance value (Asymp. Sig.) has the information we're looking for. The lower the significance value, the less likely it is that the two variables are independent (unrelated). In this case, the significance value is so low that it is displayed as .000, which means that it would appear that the two variables are, indeed, related.