The populations have the same variance 2 you can use

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Unformatted text preview: ndependent simple random samples, one from each of m populations • Each population i is normally disributed about its unknown mean µi – If sample size is large enough, the Central Limit Theorem will kick-in and inferences based on sample means will be OK even if the populations distributions are not exactly normal. – If you don’t have normality, you could use a non-parametric test, such the KruskallWallis test which is based on the ranks of the y-values rather than the y-values themselves. • The populations have the same variance, σ 2 – You can use Levene’s Test (in the car library) to test for non-constant variance. 19 20 Step two: individual t-tests with correction for multiple comparisons H0 : σ1 = σ2 = σ3 > leveneTest(rate, group) Levene’s Test for Homogeneity of Variance Df F value Pr(>F) group 2 0.0028 0.9973 42 100 Since the p-value is not less than 0.05, we do not reject. Constant variance is reasonable. 80 90 ● • If we reject the overall F -test, we proceed to further analysis. • The most common tests of interest are ‘all pairwise comparisons’ (µ1 vs. µ2, µ1 vs. µ3, ..., µm−1 vs. µm,). • We can use the Bonferroni ￿ ￿ correction to m make sure the set of all tests is do...
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