Recall That Doing Many Statistical Tests Increases the Overall Chance

Question

Examlex · Accepted Answer

The Answer is To calculate the number of tests needed before our risk of making at least one Type I error reaches 50%, we can use the formula for the probability of making at least one Type I error in multiple tests:

P(at least one Type I error) = 1 - (1 - α)^n

Where α is the significance level (0.05 in this case) and n is the number of tests.

We want to find the number of tests (n) when the probability reaches 50%, so we can set up the equation:

0.5 = 1 - (1 - 0.05)^n

Solving for n, we can use logarithms:

0.5 = 1 - (0.95)^n
0.5 = (0.95)^n
log(0.5) = n * log(0.95)
n = log(0.5) / log(0.95)
n ≈ 13.51

So, we would need to do approximately 14 tests before our risk of making at least one Type I error reaches 50%.

Recall That Doing Many Statistical Tests Increases the Overall Chance

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