PS296 Chapter Notes - Chapter 16: Multiple Comparisons Problem, Type I And Type Ii Errors
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For the case of equal sample sizes we have defined: If the sample sizes differ, however, and we define nj as the number of articipants in the jth treatment (sigmanj = n) we can rewrite the equation as: which, when all nj are equal, reduces to the original form. Basically, we multiple each squared deviation by its own sample size as we go along. We do not know which number of possible alternative hypotheses is true. Ex h1: 1 = 2 = 3 4. Many different combinations, all resulting in f being significant. Multiple comparison techniques allow us to investigate hypotheses that involve means of individual groups or sets of numbers. Ex is group 1 is different from group 2 or if combo of group 1 and 2 are different from group 3. However unrestricted use of these comparisons can lead to an excessively high probability of a type i error.
