Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 641
rious correlation. One happens when the correlation between two variables is
caused by a third, independent, variable. Another occurs when two variables
covary because of sheer accident. It happens all the time. In fact, it occurs
with a known probability.
Take a random sample of, say, 30 variables in the world, measure them, and
correlate all possible pairs of those variables. (There are n(n1) pairs of 30
anything.) According to the Bonferroni rule, you should get a correlation, significant
at the p .05 level, in 5% of all cases—in 22 out of 435 pairs—just
by chance. So, if you build a matrix with 435 pairs of correlations and find
that 20 of them are significant at the .05 level or better, you can’t be sure that
this is not simply a random event.
Of course, you always have to explain why any two variables are correlated,
since correlation, by itself, never implies cause and effect. But when you go
fishing for significant correlations in a big matrix of them, and find fewer than
you’d expect by chance alone, things are even tougher.
How tough? Pick a level of significance for reporting findings in your
data—say, .05. If you have 30 variables in your analysis, and 435 tests of
covariations in your matrix, divide .05 by 435 .0001. If you report these
correlations as significant at the 5% level (the level you chose originally),
then, according to the Bonferroni rule, your report will be valid (see Koopmans
1981; Kirk 1982). This is a very, very conservative test, but it will prevent
you from making those dreaded Type I errors and reporting significant
relations that aren’t really there.
On the other hand, this will increase your chance of making Type II
errors—rejecting some seemingly insignificant relations when they really are
important. You might fail to show, for example, that certain types of exposure
are related to contracting a particular disease, and this would have negative
public health consequences. There’s no free lunch.
Consider the study by Dressler (1980). He studied a sample of 40 people in
the Caribbean island of St. Lucia, all of whom had high blood pressure. Dressler
measured nine variables having to do with his respondents’ ethnomedical
beliefs and their compliance with a physician-prescribed treatment regimen.
He reported the entire matrix of (9 8)/2 36 correlations, 13 of which
were significant at the 5% level or better.
Dressler might have expected 36 .05 1.8 such correlations by chance.
Three of the 13 correlations were significant at the .001 level. According to
the Bonferroni rule, correlations at the .05/36 .0014 level would be reportable
at the .05 level as valid. Under the circumstances, however (13 significant
correlations with only about two expected by chance), Dressler was quite justified
in reporting all his findings.
I feel that if you are doing fieldwork, and using small data sets, you should