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Not sure if I'm misunderstanding the pwr::pwr.t.test() function and result.

set.seed(1299448) g1 <- rnorm(35, 12, 3) g2 <- rnorm(35, 14, 3) t.test(g1, g2) pwr.t.test(d = ((mean(as.numeric(g1), na.rm = T) - mean(as.numeric(g2), na.rm = T)) / sqrt(((sd(g1)^2)+ (sd(g2)^2))/2)), power = .80, sig.level = .05, alternative = "two.sided")

Results

Welch Two Sample t-test data: g1 and g2 t = -2.1738, df = 63.822, p-value = 0.03343 Two-sample t test power calculation n = 59.10848 d = 0.519647 sig.level = 0.05 power = 0.8 alternative = two.sided NOTE: n is number in *each* group

So the effect is significant with a sample size of 70, but with such an effect size, a sample size of 120 would be required for 80% power.

Can someone ELI5? Sorry if this is more of a cross-validated question. I started originally thinking this was a programming/misunderstanding of the pwr package, but now I'm starting to think I just don't understand the sample size estimation/power well enough.