Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 9, Section 2 (pp. 634-639; up to ``Models for two-way tables")



  1. Literally speaking, the null hypothesis for the chi-square test is that there is no association between the two variables being considered - that is, that the distribution for the response variable (conditional or column distribution) is the same regardless of which column (population) you look at. The only alternative hypothesis that the chi-square test addresses is the one that says ``there is an association between the variables". As with other tests of significance we've used, when the P-value of the chi-square test is small we tend to doubt the null hypothesis in favor of the alternative.

    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?















  2. You should practice going from a chi-square statistic to a P-value using Table F. Find the P-value for the following chi-square statistics: