Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 609
This PRE measure of association for nominal variables is called lambda,
written either or L. Like all PRE measures of association, lambda has the
nice quality of being intuitively and directly interpretable. A lambda of .33
means that if you know the scores on an independent variable, you can guess
the scores on the dependent variable 33% more of the time than if you didn’t
know anything about the independent variable.
Chi-Square
While lambda demonstrates the intuitively compelling PRE principle, there
are problems with it. There is no way to test whether any value of lambda
shows a particularly strong or weak relationship between variables; it can take
different values depending on whether you set up the dependent variable in
the rows or the columns; and it can be very low, even when there is an intuitively
clear association between nominal variables. Lambda for table 20.4a,
for example, is just .10—that is, if you guess that all white families with children
in the United States have two parents and that all black families have one
parent, you make 10% fewer errors than if you guess that all families have two
parents.
With bivariate data on nominal variables, many researchers use 2 (chisquare).
Chi-square tells you whether or not a relation exists between or
among variables and it tells you the probability that a relation is the result of
chance. But it is not a PRE measure of correlation, so it doesn’t tell you the
strength of association among variables.
The principal use of 2 , then, is for testing the null hypothesis that there is
no relation between two nominal variables. If, after a really good faith effort,
we fail to accept the null hypothesis, we can reject it. Using this approach, we
never prove anything using statistical tests like 2 . We just fail to disprove
things. As it turns out, that’s quite a lot.
Calculating 2
The formula for calculating 2 for a bivariate table is the same as the one
we saw in chapter 19 for a univariate distribution. Here it is again:
2 (OE)2
Formula 20.6
E
where O represents the observed number of cases in a particular cell of a
bivariate table, and E represents the number of cases you’d expect for that cell
if there were no relation between the variables in that cell.