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Multiple testing Overview

# Multiple testing Overview - Multiple testing Multiple...

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Multiple testing / Multiple comparison --Overview From Glantz, Primer of Biostatistics, Chapter 4 Suppose that we perform 5 t-tests, each with alpha = 0.05. What is the probability that we will get at least one false positive result? P(at least one false positive result) = 1 - P(zero false positive results) The probability of getting a false positive result for a single test is alpha = 0.05. So the probability of not getting a false positive result for a single test is 1 – alpha = 1 - 0.05 = 0.95. If we do k = 5 t-tests, the probability of getting no false positives on any test is 0.95^k = 0.95^5 P(at least one false positive result) = 1 - P(zero false positive results) = 1 – (1 - .05) ^ k = 1 – (1 - .05) ^ 5 = 1 – (.95) ^ 5 = 0.226 If we do 10 t-tests with alpha = 0.05, then P(at least one false positive result) = 1 – (.95) ^ 10 = 0.40 If we do 20 t-tests with alpha = 0.05, then P(at least one false positive result) = = 1 – (.95) ^ 20 = 0.64 What if we do 100 t-tests with alpha = 0.05, for 100 genes? Then P(at least one false positive result) = 1 – (.95) ^ 100 = 0.994

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We will often be interested not just in the probability of one error, but in the expected total number of errors. The expected number of false positives is simply alpha multiplied by the number of tests: For k=100 independent t-tests with alpha = 0.1, the expected number of false positives is 100 * 0.10 = 10 false positives. Family-wise error rate The probability that we will get at least one false positive result, P (at least one false positive result), is called the Family-wise error rate (FWER). Protecting against false positive results Many statistical methods have been developed to protect against making a false positive conclusion. We’ll examine the Bonferroni correction and Holm’s test.
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Multiple testing Overview - Multiple testing Multiple...

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