# Finding the beta risk from the alpha risk

Hello,
I would like to know the procedure in order to find the beta risk once the hypothesis test has been made.

I am aware of the fact that it is efficient to set both alpha and beta prior to data collection, but, in this case, I was given the observations and an alpha value. I used the t-test to compare the means, and one of the requirements is to test the hypothesis that the variances are the same. From the information that I have, the p-values and F-values do not allow the rejection of the null, which makes it possible to pool the variances and calculate the t-statistic for the first hypothesis. I understand how the alpha and beta risks are pictorially represented and what they mean, but unfortunately I don't see how to get this.

The answer to this question would be useful; it would be possible to state the risk of having assumed equal variances.

Any help is highly appreciated.

EnumaElish
Homework Helper
If you have a critical value and a distribution (i.e. a mean and a variance) then you should be able to calculate both the "alpha" and the "beta" -- by which I am assuming you mean Type I and Type II errors. Can you explain a little?

Is this homework?

No. This is not homework. I'm using a computer program to analyze data. Just an alpha value (5%) was provided along with it. I am trying to find the procedure used to calculate the correspondent beta. Yes, alpha and beta stand for Type I and II errors, respectively. I can't just pick a value and say it is true. There must be some mathematical explanation (since the value was not predetermined).

EnumaElish
Homework Helper
Since you know alpha, you know the critical value: given the location (mean) and the spread (variance) of the distribution, the "z" value that equates the tail probability to your alpha value is the critical value zc.

EnumaElish