# “effect size is independent of sample size” really?

I keep reading "effect size is independent of sample size" on the interwebs. Don't get me wrong, I get the practical vs statistical significance considerations. What I don't get is that;

-power,significance-level, sample size and effect size are all linked functionally. Fix three and you can determine the fourth.

The point is that if you fix the power and the significance-level and you increase the sample size; the effect size will also functionally change. This trivial exercise can easily be verified in GPOWER.

So researchers with little knowledge and plugging values into the likes of GPOWER can get suspicious outcomes. If a ridiculously large sample size was entered in combination with reasonable power and significance-levels (0.8 and 0.05), then the effect size would mathematically be tiny. As an effect size represents "practical significance", this would show how such a situation can be manipulated.

So why is "effect size" always referred to as being "independent of sample size" when functionally it clearly is actually dependent?

I feel the expression I keep reading should rather be stated:

effect size should be designed to be independent of sample size (or similar)

• If you fix others, what you get is the minimum effect size that your study can detect as statistically significant at a given level of power. This is not the same as the effect size you will observe from your study which is "independent" of sample size. – Heteroskedastic Jim Nov 1 '18 at 10:36