I am looking to understand alpha error calculation given power, sample size, and effect in a two-sided independent mean comparison. So the hypothesis is:

H0: mean1 = mean2 H1: mean1 != mean2

Assume we know the power, sample sizes, means and standard deviations for each group. From standard deviations, we can calculate a pooled standard deviation, and given means and pooled deviation, we can calculate effect size. Then, from there we can calculate non-centrality parameter.

I am good until this point. But from then on, for a two-tailed t-test, I am not sure how to go about reaching critical t value and find alpha.

I am looking into either an explanation or any type of resource that helps me calculate this by hand. I am aware that I can do this via G*Power:

  1. Selecting t-test family
  2. Means:Difference between two independent means (two groups)
  3. Type of power analysis: Criterion - Compute required alpha-given power, effect size, and sample size.

However, there is no explanation step by step how this is calculated for a two-sided test and I am very confused. I would like to understand this better.

Any help is appreciated.


2 Answers 2


The alpha is not calculated. Instead it is a setting of the hypothesis testing procedure that is set in advance of the analysis. It is not data-dependent and is chosen by the analyst.

It sounds like you should be looking for background reading on the topics of statistical testing. Try these posts and papers:

  • $\begingroup$ I was rather asking how criterion:alpha under GPower software is calculated given power, sample size and effect size. I am aware you choose your alpha when running a test. Again, was asking how GPower is back solving for alpha, under Criterion tests. $\endgroup$
    – kukushkin
    Commented Jul 27, 2022 at 22:16

Alpha can be solved by central and non central t distributions generated. Noncentral t distribution affects the beta (type II error) and central t distribution affects the alpha (type I error). Given sample sizes for control and treatment, as well as power and means, a greedy algorithm can solve for t critical, which can then be converted via central t distribution, into a alpha error probability value.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.