1. Use x^{2} to see how often you could expect to find the differences you see in the table just by chance. Calculate odds ratios to measure the strength of relationships.

2. Use G (or tau, or—in the case of 2 X 2 tables—Yule’s Q) to measure the association between two ordinal variables.

In actual practice, ordinal variables with seven ranks are treated if they were interval variables. In fact, many researchers treat ordinals with just five ranks as if they were intervals, because association between interval-level variables can be analyzed by the most powerful statistics—which brings us to correlation and regression.

CORRELATION: THE POWERHOUSE STATISTIC FOR COVARIATION

When at least one of the variables in a bivariate relation is interval or ratio level, we use a measure of correlation: Spearman’s r, written r_{s} when the data are rank ordered; Pearson’s product moment correlation, written simply as r, to measure the strength of linear relations; or eta squared (eta is the Greek letter ^, pronounced either eat-a or ate-a) to measure the strength of certain kinds of nonlinear relations. (Go back to the section on ‘‘shape of relation’’ at the beginning of this chapter if you have any doubts about the concept of a nonlinear relation.)