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ch. 10_102610

# ch. 10_102610 - Discussion section 227 ANOVA(Analysis of...

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Discussion section 227 10/26/10 ANOVA (Analysis of Variance) Overview ANOVA is a procedure we use to test the null hypothesis when we want to evaluate the mean differences between two or more groups. The main advantage of ANOVA is that we can make multiple comparisons between groups while keeping the alpha level constant. Hypotheses H 0 : µ 1 = µ 2 = µ 3 H 1 : At least one population mean is different The F statistic The ratio for the F statistic is similar to the t-statistic but uses variance differences instead of mean differences Variance is computed by dividing SS (sum of squares) by df (degrees of freedom) ܨ= ܸܽݎ݅ܽ݊ܿ݁ ܾ݁ݐݓ݁݁݊ ݏܽ݉݌݈݁ ݉݁ܽ݊ݏ (݃ݎ݋ݑ݌ݏ) ܸܽݎ݅ܽ݊ܿ݁ ݓ݅ݐℎ݅݊ ݃ݎ݋ݑ݌ݏ (݁ݔ݌݁ܿݐ݁݀ ݀ݑ݁ ݐ݋ ܿℎܽ݊ܿ݁ ݋ݎ ݁ݎݎ݋ݎ) This can also be stated in another way: ܨ= ܶݎ݁ܽݐ݉݁݊ݐ ݂݂݁݁ܿݐ+݂݂݀݅݁ݎ݁݊ܿ݁ݏ ݀ݑ݁ ݐ݋ ܿℎܽ݊ܿ݁ ܦ݂݂݅݁ݎ݁݊ܿ݁ݏ ݀ݑ݁ ݐ݋ ܿℎܽ݊ܿ݁ If the null hypothesis is true, the there will be no treatment effect and the ratio would be F=1 Formulas Sums of Squares ܵܵ ௕௘௧௪௘௘௡ =݊σ(ܯ−ܩܯ) GM is the grand mean ܵܵ ௪௜௧௛௜௡ = σܵܵ σ(ܺ−ܯ) For each group ܵܵ ௧௢௧௔௟ =σ(ܺ−ܩܯ) Degrees of freedom ݂݀ ௕௘௧௪௘௘௡ =ܭ−1 K is the number of groups (means) ݂݀ ௧௢௧௔௟ =ܰ−1=݂݀ ௕௘௧௪௘௘௡ +݂݀ ௪௜௧௛௜௡ N is the total number of people in the study ݂݀ ௪௜௧௛௜௡ =σ(݊−1)=σ݂݀=ܰ−ܭ

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Notice that because the total variance is sectioned into variance between and within groups, the two portions must then add back to the total: SS between +SS within = ss total df
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ch. 10_102610 - Discussion section 227 ANOVA(Analysis of...

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