8 multcomp

# 8 multcomp - Subsequent Inferences for one-way ANOVA • if...

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Unformatted text preview: Subsequent Inferences for one-way ANOVA • if the overall F test does not show significant differences among the groups, no further infer- ences are required • if the overall test does show a significant difference, differ- ences between particular means can be tested using T = ¯ x i.- ¯ x k. √ MSE r 1 n i + 1 n k • in these expressions, MSE is the estimate of σ 2 , and the degrees of freedom are N- a , the same as for MSE • however, adjustments must be made for simultaneous in- ference i.e. for the fact that several tests are being done • the simplest adjustment is the Bonferroni correction , which reduces the significance level for each test so that the overall significance level is no larger than the desired level • in a one-way ANOVA with a groups, there are r = a 2 natural comparisons between pairs of groups • if you do r tests at level α , then the probability of rejecting at least one H incorrectly could be as large as rα 1 – for example for r = 2 P ( reject at least one H ) = P ( reject 1 st ) + P ( reject 2 nd )- P ( reject both ) ≤ 2 α • to control the overall level, or experimentwise error rate , at α , each test should be done using α * = α/r • alternatively the P value should be...
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8 multcomp - Subsequent Inferences for one-way ANOVA • if...

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