# How to compute the power of a test comparing two population means (in Python, using statsmodels)

See all solutions.

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?

## Solution

From statsmodels, we use the solve_power function in the TTestIndPower class. That function 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 to perform. Let’s get started by importing the package and create a TTestIndPower object.

1
2
from statsmodels.stats.power import TTestIndPower
analysis = TTestIndPower()


For this example, let’s say that:

• You plan to create a balanced $4\times2$ factorial experiment with 32 subjects.
• You expect the effect size for the main effect of factor A to be medium (0.25 according to Cohen’s 1988 text).
• 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
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 solve_power will compute it for us:
analysis.solve_power( effect_size=effect, power=None, nobs1=obs, ratio=ratio, alpha=alpha )

1
0.1662985260871502


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.