Sidak reported an equation for estimating the probability value of statistical significance (p-value) required for individual tests that will allow for a target p-value to be achieved when all of the tests are used together.
= 1 - ((1 - (overall p value)) ^ (1 / (number of tests)))
If all of the tests have a p-value less than the target then the overall p-value will be less than its cutoff. In the real world a p-value might exceed the target if there was another test that would compensate for the change.
On the other hand, if there are multiple tests with a certain p-value, the final overall p-value if there are combined is:
overall p-value for a number of tests used together =
= 1 - ((1 - (p value for test))^(number of tests))
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