Russel-Research-Method-in-Anthropology

592 Chapter 19
Suppose that among 14 families there are a total of 42 children. If children
were distributed equally among the 14 families, we’d expect each family to
have three of them. Table 19.13 shows what we would expect and what we
might find in an actual set of data. The 2 value for this distribution is 30.65.
Finding the Significance of 2
To determine whether this value of 2 is statistically significant, first calculate
the degrees of freedom (abbreviated df ) for the problem. For a univariate
table:
df the number of cells, minus one
or 14113 in this case.
Next, go to appendix D, which is the distribution for 2 , and read down the
left-hand margin to 13 degrees of freedom and across to find the critical value
of 2 for any given level of significance. The levels of significance are listed
across the top of the table.
The greater the significance of a 2 value, the less likely it is that the distribution
you are testing is the result of chance.
In exploratory research, you might be satisfied with a .10 level of significance.
In evaluating the side effects of a medical treatment you might demand
a .001 level—or even more. Considering the 2 value for the problem in table
19.13, the results look pretty significant. With 13 degrees of freedom, a 2
value of 22.362 is significant at the .05 level; a 2 value of 27.688 is significant
at the .01 level; and a 2 value of 34.528 is significant at the .001 level. With
a 2 of 30.65, we can say that the distribution of the number of children across
the 14 families is statistically significant at better than the .01 level, but not at
the .001 level.
Statistical significance here means only that the distribution of number of
children for these 14 families is not likely to be a chance event. Perhaps half
the families happen to be at the end of their fertility careers, while half are
just starting. Perhaps half the families are members of a high-fertility ethnic
group and half are not. The substantive significance of these data requires
interpretation, based on your knowledge of what’s going on, on the ground.
Univariate numerical analysis—frequencies, means, distributions, and so
on—and univariate graphical analysis—histograms, box plots, frequency
polygons, and so on—tell us a lot. Begin all analysis this way and let all your
data and your experience guide you in their interpretation. It is not always
possible, however, to simply scan your data and use univariate, descriptive
statistics to understand the subtle relations that they harbor. That will require
more complex techniques, which we’ll take up in the next two chapters.