Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 611
TABLE 20.6
A Hypothetical Census of Religious Belief in Four Groups of Native Americans
Religion
Tribe Catholic Protestants Native American Church Total
Observed frequencies
1 150 104 86 340
2 175 268 316 759
3 197 118 206 521
4 68 214 109 391
Total 590 704 717 2,011
Expected frequencies
1 99.75 119.03 121.22
2 222.68 265.71 270.61
3 152.85 182.39 185.76
4 114.71 136.88 139.41
had collected these data, you’d now be faced with the problem of interpreting
them—that is, telling the story of how the various religions gain adherents at
the expense of the others in various places.
Suppose that instead of a census, we take a 10% random sample of the
groups—one that turns out to reflect almost perfectly the religious preferences
of the population. The results, and the expected frequencies, would look like
table 20.7.
Chi-square for table 20.7 is 15.44—still significant at the .02 level, but if
we’d taken a 5% sample, 2 would be around 7 or 8, and with six degrees of
freedom it would no longer be statistically significant, even at the .10 level.
Sample size makes a real difference here.
The Special Case of the 2 2 Table
When you have a 2 2 cross-tab of nominal data, there is an easy formula
to follow for computing 2 . Here it is:
2
n(adbcn/2) 2
(ab)(cd)(ac)(bd)
Formula 20.9
where a, b, c, and d are the individual cells shown in figure 20.2, and n is
the total of all the cells (the lower-right-hand marginal). The four sums in the