# Computing the power of Welch's t-test

I constructed a Welch's t-test in order to examine the difference between the means of two samples (check whether or not one is larger than the other).

$$H_{0}: \mu_0 = \mu_1 ~\textrm{vs}~ H_{1}: \mu_0 < \mu_1$$

I computed the t-score as follows:

$$T = \frac{\bar{x}_{0} - \bar{x}_{1}}{\sqrt{\frac{s_{0}^{2}}{n_{0}} + \frac{s_{1}^{2}}{n_{1}}}}$$

My rejection rule:

$$T < t_{\alpha, \textrm{df}}$$

Now, I would like to compute the power of this test. I know that the power is the probability of rejecting $$H_{0}$$ when $$H_{1}$$ is true. So $$P(T < t_{\alpha, \textrm{df}} | \mu_0 < \mu_1)$$.

Is that correct?

How would I compute that?

Thanks!

• For a pooled t test, a power computation requires you to specify the difference in population means and sample sizes, also guess the value of common population variance.For the Welch t test you will have specify the difference, sample sizes and make guesses about the two variances. – BruceET Mar 17 '19 at 7:53