Yesterday we shared some discussions of recent survey results on racial attitudes.
For students and teachers of statistics or research methods, I think the key takeaway should be that you don’t want to pull out just one number from a survey; you want to get the big picture by looking at multiple questions, multiple years, and multiple data sources. You want to use the secret weapon.
Where do formal statistical theory and methods come in here? Not where you might think. No p-values or Bayesian inferences in the above-linked discussion, not even any confidence intervals or standard errors.
But that doesn’t mean that formal statistics are irrelevant, not at all.
Formal statistics gets used in the design and analysis of these surveys. We use probability and statistics to understand and design sampling strategies (cluster sampling, in the case of the General Social Survey) and to adjust for differences between sample and population (poststratification and survey weights, or, if these adjustments are deemed not necessary, statistical methods are used to make that call too).
Formal statistics underlies this sort of empirical work in social science—you just don’t see it because it was already done before you got to the data.