# A power of 0.8 implies a main effect of 2.8

Can anybody please explicate the following statement by Andrew Gelman?

If you have 80% power, then the underlying effect size for the main effect is 2.8 standard errors from zero. That is, the z-score has a mean of 2.8 and standard deviation of 1, and there’s an 80% chance that the z-score exceeds 1.96 (in R, pnorm(2.8, 1.96, 1) = 0.8).

• What exactly do you find unclear about it? – Tim Feb 15 at 21:46
• Please see my answer below. I think I got confused by the code given. It is a nice trick if one wants to avoid typing lower.tail = FALSE. – Ivan Feb 16 at 7:22

In R, it could be verified by pnorm(1.96, 2.8, 1, lower.tail = FALSE), which is a more direct and verbose translation of the reasoning compared to the original code.
• Ivan, @Tim - Given that we are thinking of a two-tailed test, doesn't the code need to be something like pnorm(1.96, 2.8, 1, lower.tail = FALSE) + pnorm(-1.96, 2.8, 1, lower.tail = TRUE)? Granted, one expression or the other is likely to be negligible...or am I not thinking about this in the right way? – user697473 Mar 9 at 23:56