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STAT 301 (55)


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STAT 301
Brett Hunter

7 December ANOVA (Analysis of Variance) ANOVA allows us to compare more than two means. In case 1, we want to know if the differences in sample means can plausibly be attributed to true differences in μ , 1 ,2and μ . 3 Case 2 could be a sample from the same population used in case 1. If true, we are trying to protect against odd samples like in case 1. We call this analysis of variance since we wish to analyze the variability in the data to see how much can be attributed to differences in the μ’s and how much is due to individual variability in each individual parameter. So we have two forms of variability Variability between populations – indicates true differences in μ Variability within populations Hypotheses H 0 μ 1 μ =2… = μ k H A At least one μ diifers (at least two are different) Assumptions Each of the k populations have normal distribution. σ 1 σ =2… = σ k Each of the samples are selected independently. Observations in each sample are selected independently. ANOVA test based on SSM and SSE SSM also called SSBetween, measures disparity between sample means SSM = n ( 1 x 1 - x ) + n (2 x 2 - x ) + … + n (k xk + x )2 x ¿ x ¿i−¿ ¿ = ¿ n ¿ i k ∑ ¿ i=1 n ∑ n
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