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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 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 , then the probability of rejecting at least one H incorrectly could be as large as r 1 for example for r = 2 P ( reject at least one H ) = P ( reject 1 st ) + P ( reject 2 nd )- P ( reject both ) 2 to control the overall level, or experimentwise error rate , at , each test should be done using * = /r alternatively the P value should be...
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- Spring '12