{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Discussion4

# Discussion4 - Discussion 4 Review ANOVA Diagnostics...

This preview shows pages 1–3. Sign up to view the full content.

Discussion 4 Review: ANOVA Diagnostics Brown-Forsythe Test Recall ANOVA model is: Y ij = μ i + ij Key assumption: ij ∼ N ( 0 , σ 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 0 : σ 2 1 = σ 2 2 = · · · = σ 2 r vs. H a : Not all σ 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Step 3: The test-statistic is F * BF = MSTR MSE Step 4: Draw conclusion If F * BF > F (1 - α ; r - 1 , n T - r ), reject the H 0 Otherwise, do not reject Nonparametric Rank F Test
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

Discussion4 - Discussion 4 Review ANOVA Diagnostics...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online