How sample size calculations work

What the researchers say:

“The sample size of 102 participants will be sufficient to detect an effect size of d=0.5 or greater with 80% power and significance of 0.05”

What the researchers mean:

“We have cut & pasted this from our last application as we were short of time. The effect size of d=0.5 was chosen because Cohen said something about it being a ‘medium’ effect size and it doesn’t really relate to the hypothesis of this study at all. Even if it did, 0.5 would probably be a point estimate, so really we should have chosen the lower bounds of this estimate for the sample size calculation. This would have made the sample size very large, however, so we didn’t. Likewise, we chose 80% power and 0.05 significance because everyone else does. Hopefully no-one on the funding committee will notice the similarity of this sample size calculation to every other sample size calculation.”

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