I have a question as follows: Assuming the null hypothesis is true for all cases. If we perform mu

Eden Solomon

Eden Solomon

Answered question

2022-06-14

I have a question as follows:
Assuming the null hypothesis is true for all cases. If we perform multiple pairwise comparisons at the α = 0.05 level, what is the probability of making type I error with AT LEAST ONE of the tests?
The correct answer is greater than 0.05, and I don't know why. Thanks in advance!

Answer & Explanation

Alisa Gilmore

Alisa Gilmore

Beginner2022-06-15Added 22 answers

I may have misinterpreted the above question--please let me know if so! I do not have much of a statistical background.
The probability of not making said error in each trial is 1-.05=.95. So over n trials, you have a probability of . .95 n of the error never occurring, and the probability of it occurring at least once (this is the complement of the situation where the error never occurs) is 1-. .95 n .
But since .95 is less than 1, when n>1, we have . .95 n <.95, so 1-. .95 n >1-.95=.05 .

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