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1 Why is multiple testing a problem?

Spring 2008 - Stat C141/ Bioeng C141 - Statistics for BioinformaticsCourse Website: Website: Contact Info:Megan Hours: 342 Evans M 10-11, Th 3-4, and by appointment1 Why is multiple testing a problem? Say you have a set of hypotheses that you wish to test simultaneously. The first idea thatmight come to mind is to test each hypothesis separately, using some level of significance .At first blush, this doesn t seem like a bad idea. However, consider a case where you have20 hypotheses to test, and a significance level of What s the probability of observingat least one significant result just due to chance?P(at least one significant result) = 1 P(no significant results)= 1 (1 )20 , with 20 tests being considered, we have a 64% chance of observing at least one sig-nificant result, even if all of the tests are actually not significant. In genomics and otherbiology-related fields, it s not unusual for the number of simultaneous tests to be quite abit larger than and the probability of getting a significant result simply due to chancekeeps going for dealing with multiple testing frequently call for adjusting in some way, sothat the probability of observing at least one significant result due to chance remains belowyour desired significance The Bonferroni correctionThe Bonferroni correction sets the significance cut-off at /n.

a vector, x, of length 1000. The rst 900 entries are random numbers with a standard normal distribution. The last 100 are random numbers from a normal distribution with mean 3 and sd 1. Note that I didn’t need to indicated the sd of 1 in the second bit; it’s the default value.

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