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Unformatted text preview: 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 : 1 = 2 . The One-way ANOVA can test the equality of several population means. That is: H : 1 = 2 = 3 = = t H a : At least one of the t-population means differs from the rest. Assumptions 1. Normal populations. 2. equality of population variances, 2 1 = 2 2 = = 2 t . Test statistic: F = s 2 B s 2 W H 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 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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This note was uploaded on 01/31/2011 for the course AMS 572 taught by Professor Weizhu during the Fall '10 term at SUNY Stony Brook.
- Fall '10