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# ch8 - AMS 315/576 Lecture Notes Chapter 8 One-Way Analysis...

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¤ § ¥ ƒ AMS 315/576 Lecture Notes Chapter 8. One-Way Analysis of Variance (ANOVA) This is an extension of the pooled-variance t -test . The pooled-variance t -test tests the null hypothesis that two population means are equal, i.e. H 0 : μ 1 = μ 2 . The One-way ANOVA can test the equality of several population means. That is: H 0 : μ 1 = μ 2 = μ 3 = · · · = μ t H a : At least one of the t -population means differs from the rest. Assumptions 1. Normal populations. 2. equality of population variances, σ 2 1 = σ 2 2 = · · · = σ 2 t . Test statistic: F = s 2 B s 2 W H 0 F t - 1 ,n T - t where s 2 B = SSB t - 1 , s 2 W = SSW n T - t . Here SSB = t X i =1 n i y i · - ¯ y ·· ) 2 (Sum of squares between samples); SSW = t X i =1 n i X j =1 ( y ij - ¯ y i · ) 2 = TTS - SSB (Sum of squares within samples); TSS = t X i =1 n i X j =1 ( y ij - ¯ y i · ) 2 (Total sum of squares); 1

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TSS = X i,j y 2 ij - y 2 ·· n T SSB = X i y 2 i · n i - y 2 ·· n T SSW = TSS - SSB. y ij : The j th sample observation selected from population i . For example, y 23 denotes the third sample observation drawn from population 2.
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ch8 - AMS 315/576 Lecture Notes Chapter 8 One-Way Analysis...

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