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Unformatted text preview: Chapter 3: K-Sample Methods 0. Comparing more than two groups (treatments) overall comparison: whether or not differences exist among groups multiple comparison: which groups differ significantly from the others Assumption: the experimental units are assigned to the k treatments in a completely random design or the observations have been randomly selected from k populations Hypothesis: H : F 1 ( x ) = F 2 ( x ) = = F k ( x ) H a : F i ( x ) F j ( x ) or F i ( x ) F j ( x ) for at least one pair ( i,j ) with strict inequality holding for at least one x Shift Alternative Hypothesis: H : F 1 ( x ) = F 2 ( x ) = = F k ( x ) = F ( x ) H a : F i ( x ) = F ( x i ) for at least one i of i = 1 ,...,k 1. K-Sample Permutation F-Tests One-Way Data Layout X ij = i + ij where ij iid F ( ) N = n 1 + n 2 + + n k Treatments Observations Sample Sizes Means Variances 1 X 11 ,X 12 ,...,X 1 n 1 n 1 X 1 S 2 1 2 X 21 ,X 22 ,...,X 2 n 2 n 2 X 2 S 2 2 ... ... ... ... ... k X k 1 ,X k 2 ,...,X kn k n k X k S 2 k 1 One-Way ANOVA test Assumptions: for i = 1 ,...,k j = 1 ,...,n i X ij iid N ( i , 2 ) X i s are independent Hypothesis: H : 1 = 2 = = k H a : i negationslash = j for at least one pair ( i,j ) F test: X = k i =1 n i j =1 X ij /N Source DF SS MS F Treatment k 1 SST r = k i =1 n i ( X i X ) 2 MST = SST k- 1 F = MST MSE Error N k SSE = k i =1 ( n i...
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This note was uploaded on 07/22/2011 for the course STA 4502 taught by Professor Staff during the Spring '08 term at University of Florida.
- Spring '08