When creating a factorial design, it is important that it has adequate power to detect significant main effects and interaction effects of interest. How can we calculate the power of a two-sample $t$ test that we aim to perform in such a situation?
We use the
power.t.test function in R. It embodies a relationship among
five variables; you provide any four of them and it will compute the fifth to
be consistent with the first four, regarding the two-sample $t$-test you plan
For this example, let’s say that:
- You plan to create a balanced $4\times2$ factorial experiment with 32 subjects.
- You wish to be able to detect a difference
- You want to know the expected power for the test of a main effect of factor A.
- Your significance level is $\alpha=0.05$.
We proceed as follows.
1 2 3 4 5 6 7 8 9 10 # install.packages('pwr') # if you have not already installed it library(pwr) obs <- 32 # number of subjects (or observations) effect <- 0.25 # effect size alpha <- 0.05 # significance level ratio <- 1 # ratio of the number of observations in one sample to the other # We leave power unspecified, so that power.t2n.test will compute it for us: pwr.t2n.test(n1=obs, n2=obs, d=effect, sig.level=alpha, power=NULL)
1 2 3 4 5 6 7 8 t test power calculation n1 = 32 n2 = 32 d = 0.25 sig.level = 0.05 power = 0.1662985 alternative = two.sided
The power is 0.1663, which means that the probability of rejecting the null hypothesis when in fact it is false OR the probability of avoiding a Type II error is 0.1663.
Content last modified on 24 July 2023.
Contributed by Nathan Carter (email@example.com)