In a given situation, suppose H0 (null hypothesis) was not rejected at alpha= .02.
Would H0 also be retained at alpha = .01?
would H0 also be retained at alpha = .05?
I'm thinking yes and can't tell.
I agree
If you did not reject Ho at P = .02, You would definitely not reject it at the .01 level.
However, it is possible that it could still be rejected at the .05 level. You are allowing the probability of larger alpha error in that case.
I hope this helps. Thanks for asking.
Yes, you are correct. If the null hypothesis (H0) was not rejected at alpha = .02, it would also not be rejected at a lower significance level like alpha = .01. This is because when we use a lower alpha level, we are being more stringent in our decision making and requiring stronger evidence to reject the null hypothesis.
However, it is possible that the null hypothesis could still be rejected at a higher significance level like alpha = .05. This is because at a higher alpha level, we are more lenient in our decision making and allow for a higher probability of making a Type I error (rejecting the null hypothesis when it is actually true).
In summary, if H0 is not rejected at alpha = .02, it would also not be rejected at alpha = .01, but it could still be rejected at alpha = .05.