LL7 - Part 7 Analysis of Variance 1. One-Way ANOVA Section...

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BUS1200-7 1 Part 7 Analysis of Variance 1. One-Way ANOVA Section 7.1 One-Way ANOVA Assumption Suppose there are k ( 2) normal populations with equal variances. Population 1 2 … k Mean µ 1 2 k Variance σ 2 2 2 The hypotheses considered are H 0 : 1 = 2 = = k and H 1 : not all population means are equal. Examples of WRONG H 1 : at least one of the i ’s is not equal to the others all i ’s are different 1 2 k BUS1200-7 2 If we draw independently a random sample from each of the k populations, then we will have the following table: Sample 1 2 … k Overall x 11 x 12 x 1 k x 21 x 22 x 2 k M M M M 2 2 n x M 1 1 n x M k n k x Total t 1 t 2 t k t Mean 1 x 2 x k x x Variance s 1 2 s 2 2 s k 2 where, for j = 1, 2, …, k , () = = = = = j j n i j ij j j j j j n i ij j x x n s n t x x t 1 2 2 1 , 1 1 , , and . , , 1 1 n t x n n t t k j j k j j = = = = = Note that x is the weighted average of all sample means with the weights being the sample sizes. BUS1200-7 3 Definition 1. The total sum of squares , denoted by SST , is ∑∑ == k j n i ij j x x 11 2 .
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LL7 - Part 7 Analysis of Variance 1. One-Way ANOVA Section...

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