The Practice of Social Research
Chapter Sixteen. Social Statistics
Inferential Statistics
Univariate Inferences
Tests of Statistical Significance
The Logic of Statistical Significance
Chi Square
The descriptive statistics discussed so far in this chapter was just that:
descriptions of the data being analyzed, such as the responses to a sample
survey. Inferential statistics aim to determine whether the
results observed among the data represent something genuine in the real world
or are simply artifacts of the research.
Let's say sample survey of voters indicates that Candidate A will receive
55 percent of the vote. As we say in Chapter 7, such a finding is only
an estimate, which can be swayed by the vagaries of sampling error. Univariate
inferences indicate how closely the sample estimates are likely to come
to the voting intentions of all the voters.
Much of this chapter deals with the issue of statistical significance.
If a relationship is observed between two variables in the data collected
in a sample survey, that relationship either represents (1) a genuine relationship
in the world or (2) the happenstance of sampling error. If we find
women more religious than men in the sample data, that could simply
mean our sample happened to get too many religious women and too few religious
men. A relationship is judged to be statistically significant if it
is extremely unlikely for it to have resulted from sampling error alone.
We take time to illustrate the calculation of statistical significance
by way of a commonly-used test: chi square.
While tests of statistical significance serve an important role in social
research, it is important to distinguish statistical from substantive
significance. We could, for example, design a large and sophisticated
sample that severely narrowed the range of sampling error; if we found women
slightly more likely to vote for Candidate A than men, we would be highly
confident that there was a very small relationship between sex and voting.
The observed difference would be statistically significant (certain
to exist among all voters, not just the sample) but it would be of little
or not sibstantive importance.
Finally, it is important to always remember that statistical significance
relates exclusively to sampling error. Unless the data being analyzed
resulted from a sample selection process, tests of statistical significance
are inappropriate. For example, in those cases were a whole population
is being studied, tests of statistical significance are not appropriate.
If 57 percent of the women and 53 percent of the men say they will
vote for Candidate A, that's it. We are not estimating the population;
we know what's so.