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14 mult2way1

# 14 mult2way1 - Subsequent Inferences for two-way ANOVA the...

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Subsequent Inferences for two-way ANOVA the kinds of inferences to be made after the F tests of a two-way ANOVA depend on the results if none of the F tests lead to rejection of the null hypothesis, then you have concluded that none of the means are different and no further comparisons are required Significant interactions if it has been determined that the interactions are significant, then the effect of each factor depends on the level of the other factor another way of saying this is that each cell of the table has a possibly different mean μ ij there are IJ such means and r = IJ 2 ! possible comparisons among them

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to control the overall type 1 error rate at α , the Bonferroni correction uses α * = α/r for each comparison confidence intervals have the form ¯ y ij. - ¯ y kl. ± t IJ ( K - 1) α * / 2 MSE q 2 /K tests of H 0 : μ ij = μ kl versus H a : μ ij 6 = μ kl are based on the statistic t ij,kl = ¯ y ij. - ¯ y kl. MSE q 2 /K the null hypothesis is rejected when P < α * or when | t ij,kl | > t IJ ( K - 1) α * / 2 it is often easiest to rearrange this expression and reject H 0 when | ¯ y ij. - ¯ y kl. | > t IJ ( K - 1) α * / 2 MSE q 2 /K the right hand side remains constant so it is just a matter of looking at the differences between any two cell means
Example: The following data are the lifetimes (in hours) of four different designs of an airplane wing subjected to three different kinds of contin- uous vibrations.

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14 mult2way1 - Subsequent Inferences for two-way ANOVA the...

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