On p. 639, you can see the detailed calculation of the chi-square statistic for the table of Example 9.8 (p. 635). After this calculation, the authors turn to Table F and find the appropriate P-value (P < 0.001 in this case). Since this is such a small P-value, it seems reasonable to reject the null hypothesis in favor of the alternative which, in this case would be that there is an association between economic status (SES) and smoking. That, of course, is what the sample showed, but we have (by means of the test) found some support for thinking that what was clearly true about the sample also is likely true about the population. This is because the test showed that differences in the conditional distributions as extreme as what we see in our sample would be quite unlikely to arise in samples (random samples with the same column and row totals as ours) if the null hypothesis of no association were true.

Now that we feel confident that there is an association, how do we make the jump to saying (as the authors have) that, in general, smoking seems to decrease as economic status increases? Is that a result of the chi-square test as well?

The test itself only leads to the conclusion that there is an association. At this point, if we want to know what the association actually is, we must look at the data. Graphs are helpful here. The bar graphs on p. 637 (Figure 9.4) show us the conditional distributions (three in all, one for each SES level) for the data on p. 635. It is these bar graphs that seem to suggest the relationship of ``smoking goes down as SES rises". By the way, the authors refer to this as a negative association, which means that one variable rises as the other one falls.

• c² = 11.5, where you have a 3-by-3 two-way table.
• c² = 28.26, where you have a 3-by-9 two-way table.
• c² = 6.71, where you have a 6-by-2 two-way table.

Answers: 0.02 < P < 0.025, 0.025 < P < 0.05 and 0.2 < P < 0.25 respectively.