This chapter is about describing relations between pairs of variables—covariations—and testing the significance of those relations.

The qualitative concept of covariation creeps into ordinary conversation all the time: ‘‘If kids weren’t exposed to so much TV violence, there would be less crime.’’ Ethnographers also use the concept of covariation in statements like: ‘‘Most women said they really wanted fewer pregnancies, but claimed that this wasn’t possible so long as the men required them to produce at least two fully grown sons to work the land.’’ Here, the number of pregnancies is said to covary with the number of sons husbands say they need for agricultural labor.

The concept of statistical covariation, however, is more precise. There are two primary and two secondary things we want to know about a statistical relation between two variables:

The primary questions are these:

1. How big is it? That is, how much better could we predict the score of a dependent variable in our sample if we knew the score of some independent variable? Correlation coefficients answer this question.

2. Is the covariation due to chance, or is it statistically significant? In other words, is it likely to exist in the overall population to which we want to generalize? Statistical tests answer this question.

For many problems, we also want to know:

3. What is its direction? Is it positive or negative?

4. What is its shape? Is it linear or nonlinear?

Answers to these questions about qualities of a relationship come best from looking at graphs.

Testing for statistical significance is a mechanical affair—you look up, in a table, whether a statistic showing covariation between two variables is, or is not statistically significant. I’ll discuss how to do this for several of the commonly used statistics that I introduce below. Statistical significance, however, does not necessarily mean substantive or theoretical importance. Interpreting the substantive and theoretical importance of statistical significance is anything but mechanical. It requires thinking. And that’s your job.