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lecture 11

# lecture 11 - ASSUMPTIONS of ANOVA equal variances(required...

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ASSUMPTIONS of ANOVA: equal variances (required for pooling) normality (required for test distribution) The null hypothesis in ANOVA is always: This implies that any combination of means are also equal 1 2 3 j μ μ μ μ = = = 1 2 3 ( ) / 2 μ μ μ + = The alternative hypothesis in ANOVA is always - The population means are different (at least one mean is different from another)

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**** Null hypothesis is tested by comparing two estimates of the population variance ( σ 2 ) : (MS B ) between-group estimate of ( σ 2 ) AFFECTED by whether the null is true (MS W ) within-group estimate of ( σ 2 ) UNAFFECTED by whether the null is true .
-- when the null hypothesis is true (MS B ) F ratio = ------- = About 1 (MS w ) -- when the null hypothesis is not true (MS B ) F ratio = ------- = Much greater than 1 (MS w )

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S 2 _ X (n) estimates σ 2 just as well as any random samples would S 2 _ X (n) = MS B will be higher than the populations variance because the means are farther away from each other than would be expected by chance If Null is true, then these are just random samples If Null is false, then these are not just random samples Between Groups variance
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