I encounter an issue when trying to calculate sample size for a two-sample t test, which may due to very large mean and very small variance of the data. Suppose I have some control group data simulated as below:
set.seed(1) x = rnorm(10, 1000, 1)
And from prior knowledge, treatment group has a 10% larger mean than control group. Significant level is 5%, power is 80%. Per my understanding, effect size can be calculated as
D = mean(x)*10%/sd(x) # 1281.258
Clearly, this effect size is too large, and if I use package 'pwr' to sample size n
pwr.t.test(d = D, power = 0.8, sig.level = 0.05, type = 'two.sample')
Function returns error due to this large effect size.
So, in such a situation, is there a way to calculate sample size, maybe by transforming data or something else; or do I even need to calculate sample size since 10% of mean is quite large to variance, and people can easily tell which group the data come from?