I'm trying to find the power of a paired t-test. I used the power.t.test function, but noticed that if I increase the p-value, the power also increase. I do not understand, should not the power decrease, when the p-value increase?
power.t.test(n = 33, delta = 0.5, sd = 1, sig.level = 0.05,
power = NULL,
type = "paired",
alternative = "two.sided",
strict = T)
power=0.80
power.t.test(n = 33, delta = 0.5, sd = 1, sig.level = 0.45,
power = NULL,
type = "paired",
alternative = "two.sided",
strict = T)
power=0.98
I assume you mean the significance level with p value?
Keep in mind that the statistical power is the probability to reject H0 if H1 is correct, I.e. the the probability to recognise a true difference. Your significance level is the threshold which you use to decide which hypothesis to accept, if p < sig. level, H1 will be accepted. A lower significance level decreases the risk of wrongly accepting H1 (Type 1 error, I.e. to assume a difference when there is none), but at the same time it increases the risk for a type 2 error (failure to reject a false H0, I.e. failure to recognise a true difference). Conversely, an increased significance value increases the statistical power since it makes it more likely that H0 is rejected.
I hope that explanation works for you, it’s not always easy for me to explain statistical concepts in a conscience way..