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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 kickin 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 nonparametric test, such the KruskallWallis test which is based on the ranks
of the yvalues rather than the yvalues
themselves.
• The populations have the same variance, σ 2 – You can use Levene’s Test (in the car library) to test for nonconstant variance. 19 20 Step two: individual ttests 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 pvalue 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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 Winter '13
 Sun
 Statistics, Linear Regression, Variance

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