Data Analysis with Microsoft Excel: Updated for Office 2007

306 Fundamentals of Statistics

It’s interesting to note that those statistics which do not assume that the

data are ordinal (the Pearson chi-square, the continuity-adjusted x^2 , and the

likelihood ratio x^2 ) all fail to reject the null hypothesis at the 0.05 level. On

the other hand, the statistics that take advantage of the fact that we’re using

ordinal data (the Goodman-Kruskal gamma, Kendall’s tau-b, Stuart tau-c,

and Somers’ D) all reject the null hypothesis. This illustrates an important

point: Always use the statistics test that best matches the characteristics of

your data. Relying on the ordinal tests, we reject the null hypothesis, ac-

cepting the alternative hypothesis that the pattern of enrollment differs on

the basis of whether calculus is a prerequisite.

To explore how that difference manifests itself, let’s examine the table of

expected values and standardized residuals in Figure 7-27.

Figure 7-27
Expected counts
and standardized
residuals for the
enrollment table

From the table, we see that the null hypothesis underpredicts the number

of courses with class sizes in the 1–50 range that require knowledge of calcu-

lus. The null hypothesis predicts that 12.37 classes fi t this classifi cation, and