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