Statistical Measures

Using Chi-square For every correlation you discuss, you should note whether it is statistically significant. Chi-square does this for you. Your printout has several figures related to Chi-square; the only one appropriate for our purposes is the Pearson Chi-Square Asymptotic Significance figure, which we will simply call the chi-square significance figure. It is nearly always smaller than 1.0000. Social scientists agree that .05 or smaller indicates a statistically significant correlation, one unlikely to have occurred by chance; we will adhere to that standard in this course.

Descriptive statistics: Kendall's tau and Cramer's V These two statistical tests are among several that test the strength of the relationship between variables. Kendall's tau is used when all variables involved are ordinal, which means they have direction or order, such as age or education. You may assume any two-value variable to be ordinal. In the SPSSX package we are using, you have the option of selecting Kendall's tau-b or Kendall's tau-c; tau-b is for square tables and tau-c is for rectangular ones. Cramer's V is used with nominal variables, those without order, such as race or region.

Translating Kendall's tau and Cramer's V Values (Be extremely wary of positive and negative correlations. SPSSX doesn't know whether they make sense or not. It simply notes whether the dependent variable's values rise with the independent variable's values.)

The appropriate phrase for Kendall's tau and Cramer's V values:

• .50 or higher a very strong relationship
• .36 to .49 a substantial relationship
• .20 to .35 a moderate relationship
• .10 to .19 a low relationship
• .00 no relationship

Remember: You are expected to use both Chi-square and Kendall's tau or Cramer's V (whichever is appropriate) to characterize every relationship you test.