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Unformatted text preview: STATISTICS 211 PROF EMANUEL PARZEN CHAPTER 8 ANALYSIS OF VARIANCE, MULTIPLE SAMPLES Statistical methods for learning from multiple (more than 2) samples is called Analysis of Variance; they were pioneered by Sir Ronald Fisher in the 1920/s. We observe a response variable Y (assumed to be continuous quantitative) from multiple popu lations represented by levels of another variable, which we in dex by variable X , with c possible values representing catego ries, populations, levels. The observed data is summarized by sample sizes, means, variances with notation given in the following table. I. SUMMARY original data by sample sizes. means, variances I X levels Sample size i n Sample Mean Sample St. Dev. 1 1 X 2 2 X ⋮ ⋮ c c X 1 2 c n n n ⋮ c ( 29 c ( 29 c ( 29 1 1 2 2    c c Y Y X Y Y X Y Y X μ μ μ = = = i i i ⋮ 1 2 c S S S ⋮ Pooled Sample has size : 1 2 c n n n n = + + + ⋯ , Grand Mean c ( 29 Y Y μ ⋅⋅ = ; pooled estimator of standard deviation de noted pool S or S, defined by...
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 Fall '07
 Parzen
 Statistics, Variance, Sir Ronald Fisher, PROF EMANUEL PARZEN, SSTr SSTo MSE, variances Sample size, Variance Table Source

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