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Unformatted text preview: Discussion 4 Review: ANOVA Diagnostics Brown-Forsythe Test Recall ANOVA model is: Y ij = i + ij Key assumption: ij N ( , 2 ) i.e. for all factor levels, the variances of the errors should be the same Usually before fitting the model we, should examine the constancy of error vari- ance, using Brown-Forsythe Test , which test: H : 2 1 = 2 2 = = 2 r vs. H a : Not all 2 i are equal Step1: Defining d ij = | Y ij- Y i | Y ij is the j th observation in the i th factor level. Y i is the median of the i th factor level Step 2: Define MSTR & MSE MSTR = r i =1 n i ( d i - d ) 2 r- 1 MSE = r i =1 n i j =1 ( d ij- d i ) 2 n T- r where d = n i j =1 d ij n i d = r i =1 n i j =1 d ij n T (Here we just simply replace Y by d in normal F-test to get MSTR and MSE for Brown-Forsythe test) 1 Step 3: The test-statistic is F * BF = MSTR MSE Step 4: Draw conclusion If F * BF > F (1- ; r- 1 ,n...
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This note was uploaded on 11/17/2010 for the course CHEM2A CHEM taught by Professor Enderle during the Spring '05 term at UC Davis.
- Spring '05