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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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