The problem is noise, not N: why increasing the sample size isn’t all that.

Someone was talking with me about the problem with lots of published social science research that’s based on small sample sizes. And I agree that this is a problem! But I think the real problem is noise, not N.

Noise (variation in effect size, variation in outcomes, and measurement error) is more of an issue than sample size because lots of bad studies are so noisy that, to get a large enough sample size to detect a reliable effect, you’d need N = a zillion, and at that point you’d be averaging over such a wide range of conditions that it’s not clear what you’re estimating anyway.

There’s a widespread misunderstanding by which people think that their problems can be solved with bigger samples. I think the erroneous reasoning goes like this: People are aiming for 80% power, but they really have only 50% power, or 30% power, or something like that. If you have 50% power and double your sample size, you’ll have 80% power . . . a win! The error in this reasoning is that often the power is much less than 50%, more like 5% + epsilon. The flip side of this is that if you really are running studies with 50% power or even 30% power, you’re likely to get the right direction on the effect size anyway, so often there’s no good reason to wait on statistical significance.

So, lots of moving parts here: There’s the underlying effect size, the variation in effect size, the variation in the measured outcomes, and researchers’ expectations when setting effect sizes and interpreting results.