Statistical Power for Two Samples T-Test

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• #240751

mleon
Participant

Hello! I have a population, I randomly assign half of them to one procedure and the others to a second procedure. I like to test if the two procedures are the same. I conduct 2 samples t test and the p value is 0.616. When I test the statistical power for the results of my teo groups, it is calculated to 7.3%. Am I Sure that the two procedures do not differ? In other words, refardless of the low statistical power, am I sure not making type II errors?

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#240799

Robert Butler
Participant

Something doesn’t seem right.  I would like to check the calculation. Could you post your total sample size and the values of the two averages?

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#240825

Chuck White
Participant

Type II error is fuzzier than Type I error. To quantify beta risk (and power), you have specify the difference of interest (how big a difference needs to be to have practical importance). You can never be confident that there is zero difference without testing the entire population, but power and sample size calculations give you the probability that you will reject the null hypothesis if the actual difference is greater than your difference of interest. If the difference of interest you choose is small compared to the standard error, you will get a low power (as you did). If you truly want to be able to detect a difference this small, your current test is not sufficient — you will likely need a much larger sample size. On the other hand, if the difference you specified is too small to have any practical importance, determine what that practical difference actually is and rerun the calculation.

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