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.