I know that significance tests don't make sense on population data. But how then can I figure out if effect sizes are meaningful? Is it purely a judgement call?

Background: I have a census for an entire population. I want to look at correlations between income and the different things studied in the population, e.g. income vs education level, income vs religion, income vs family size, etc.

I will calculate correlations for all the variables across incomes, and look at the ones with the highest correlations.

However, with enough variables, one would assume that at least some of the correlations would then be due to chance, and who knows, perhaps all of them are due to chance.

Is there any way to account for this, and state whether there is more or less chance than we would expect? Or do I just have to report the results as I find them, and let the reader draw their own conclusions about whether they are purely chance?


There is no sampling going on here so there is no "chance correlations" going on here. You would simply declare a certain correlation as large enough to be meaningful before looking at your data. Then, you would look at your censuse figures and any one that is larger than the one you established should be noted. Since this is a census, you just report the results. There is no sampling variability in the responses.

Now, whether or not there is measurement error, is an entirely different question. . .

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