Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 615
where a, b, c, and d are the actual contents of the four cells in the 2 2 table
(see figure 20.2 above) and n is the total number of cases. An exclamation
point signifies the factorial of a number, or the product of a sequence of numbers.
So, 4! is four-factorial, or 4 3 2 1 24. Calculators can’t
handle the factorials of large numbers, but you can do the needed calculations
on a spreadsheet when you have the relatively small numbers involved in a
Fisher’s exact test.
The exact probability of observing the particular distribution of cases in
table 20.9 is:
p (362,880)(720)(40,320)(5,040)
(1,307,674,368,000)(5,040)(2)(1)(120) 0.033566434
For a one-tailed test of the null hypothesis, we need to add this probability to
the probability of finding any other distributions that are more extreme than
the one in the actual data. There is one configuration of these data that is more
extreme: a 8, b 0, c 1, and d 6 (where a, b, c, and d are the cells
in figure 20.2). The exact probability of that distribution is 0.001398601. For
a one-tailed test, we add these probabilities:
0.033566434 0.001398601 0.034965
A two-tailed test is simply twice this probability, or 0.06993. There is a
strong hint in these data that men who are above median height have more
girlfriends than are men who are below median height in this tribe. But the
case is tentative and awaits further tests on larger samples.
Gamma: The All-Purpose PRE Measure of
Association for Ordinal Variables
Once you understand the PRE principle, a lot of things in statistics fall into
place. Kempton et al. (1995) surveyed intentionally selected samples of people
in the United States whom they thought would show pro- and anti-environmentalist
attitudes. (Members of the Sierra Club, for example, are people
you’d anticipate would be pro-environmental activism, while loggers are people
you’d think would be against that kind of activity.) Here are two questions
from Kempton et al.’s study:
You shouldn’t force people to change their lifestyle for the sake of the environment.
1. Disagree 2. Neutral 3. Agree