ppose again negative correlated, so that if one is large then the other will tend to be small. How does the family-wis error rate associated with these m = 2 tests qualitatively compare to the case of independe tests? Hint: First, suppose that whenever one p-value is less than a, then the other will be greater than a. In other words, we can never reject both null hypotheses. They are the same. FWER is greater for negatively correlated tests than for independent tests

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Suppose again that m = 2, but that now the p-values for the two tests are negatively
correlated, so that if one is large then the other will tend to be small. How does the family-wise
error rate associated with these m = 2 tests qualitatively compare to the case of independent
tests?
Hint: First, suppose that whenever one p-value is less than a, then the other will be greater
than a. In other words, we can never reject both null hypotheses.
They are the same.
FWER is greater for negatively correlated tests than for independent tests
FWER is smaller for negatively correlated tests than for independent tests.
Transcribed Image Text:Suppose again that m = 2, but that now the p-values for the two tests are negatively correlated, so that if one is large then the other will tend to be small. How does the family-wise error rate associated with these m = 2 tests qualitatively compare to the case of independent tests? Hint: First, suppose that whenever one p-value is less than a, then the other will be greater than a. In other words, we can never reject both null hypotheses. They are the same. FWER is greater for negatively correlated tests than for independent tests FWER is smaller for negatively correlated tests than for independent tests.
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