Two contingency tables below show return on investment (ROI) and percent of sales growth over the previous 5 years for 85 U.S. rms. ROI is defined as percentage of return on a combination of stockholders' equity (both common and preferred) plus capital from long-term debt including current maturities, minority stockholders' equity in consolidated subsidiaries, and accumulated deferred taxes and investment tax credits. Research question: At α = .05, is ROI independent of sales growth? Would you expect it to be? Do the two tables (2 × 2 and 3 × 3) agree? Are small expected frequencies a problem?

2 x 2 Cross-Tabulation of Companies RO Low RO High ROl Col Total Low Growth 24 14 38 High Growth 16 31 47 Row Total 40 45 85 3 x 3 Cross-Tabulation of Companies ROI Low Growth Medium Growth High Growth Row Total Low RO Medium ROI High ROl Col Total 12 14 12 38 28 27 30 85 6 17 16 31