Russel-Research-Method-in-Anthropology

614 Chapter 20
fewer than five cases expected in any cell, 2 can be distorted and there is a
danger of drawing the wrong conclusion from the data.
There are, however, 68(20)/95 14.32 cases expected of women who
report not having any personal experience with witchcraft. The fact that only
five cases actually turned up in this cell is thus strong evidence, not a cause
for worry.
When the expected number of frequencies for any cell in a 2 2 table is
less than 5, use Fisher’s exact probability test. Here’s an example.
Table 20.9 shows data from Thomas Gregor’s study (1979) of height and
social success among the Mehinaku of the Brazilian Amazon. The median
height of 15 unmarried, adult men in the tribe was 161.85 cm (just under 54).
The median number of girlfriends that each man had was four. The independent
variable in table 20.9, then, is height, measured as equal to or less than
TABLE 20.9
Data on the Number of Girlfriends by Height
161.85 161.85 cm Column totals
4 girlfriends 7 2 9
[expected] [4.8] [4.2]
4 girlfriends 1 5 6
[expected] [3.2] [2.8]
Row totals 8 7 15
SOURCE: T. Gregor, ‘‘Short People.’’ Reprinted from Natural History, Vol. 88, no. 2, pp. 14–21. Copyright
Natural History Magazine, Inc., 1979. Reproduced by permission.
the median, or greater than the median. The dependent variable is the number
of girlfriends, measured as equal to or less than the median, or greater than
the median.
Of the eight men who were at or below median height, seven had four or
fewer girlfriends. Of the seven men who were above median height, five had
more than four girlfriends. The expected values for each cell are shown in
brackets in table 20.9.
Since the cells have expected values of less than 5, we apply Fisher’s exact
text. There are thousands of ways to throw the expected cases (5, 4, 3, 3) into
four cells, but there are fewer ways to do it if you have to make the right-hand
marginals add up to the observed values. Given a set of fixed marginals in a 2
2 table, the probability of seeing any distribution of cases is:
p (ab)!(cd)!(ac)!(bd)!
n!a!b!c!d!
Formula 20.11