More_Than_2_Var_Means

# More_Than_2_Var_Means - 13.2 Testing More Than 2 Variances...

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1 13.2 Testing More Than 2 Variances: Bartlett’s test 13.1 Testing More than 2 Means: Analysis of Variance

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2 More than 2 Variances (from Normal Distribution) Multiple tests exist (Bartlett, Levene, Cochran, etc.). We will focus on Bartlett’s test:
3 Bartlett’s Test Hypotheses: H 0 : σ 2 1 = σ 2 2 = ... = σ 2 k H 1 : All the variances are not equal Test Statistic: Rejection Rule: Reject H 0 if b calc < b k ( α ; n 1 , n 2 ,…,n k ) where b k ( α ; n 1 , n 2 ,…,n k ) [ ] k N s n s s s s s b k i i i p p k N n k n n k - - = = = - - - - 1 2 2 2 ) /( 1 1 2 1 2 2 1 2 1 ) 1 ( ) ( * .. * ) ( * ) ( 2 1 N n b n n b n n b n k k k k k ) ; ( ... ) ; ( ) ; ( 2 2 1 1 α + + +

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4 Example: We have 4 samples of serum alkaline phosphatase activity levels for four different drugs. We want to test the equality of the variances at alpha = .01. Drug n Sample mean Sample std. deviation 1 20 73.01 25.75 2 9 48.93 47.11 3 9 93.61 46.57 4 7 101.06 30.76
5 Hypotheses: H 0 : H 1 : Test Statistic:

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6 Rejection Rule: Decision: Conclusion:
In this class, we will also use JMP output for Bartlett’s test. 7 Test F Ratio DFNum DFDen Prob > F O'Brien[.5] 0.4206 3 20 0.7402 Brown-Forsythe 0.5988 3 20 0.6232 Levene 0.6651 3 20 0.5833 Bartlett 0.3784 3 . 0.7686 If the p-value is greater than alpha for Bartlett’s test, assume the variances are equal.

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8 What if We Have More than 2 Means To Compare for a Normal Population? Suppose we want to test the average strength of paper
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More_Than_2_Var_Means - 13.2 Testing More Than 2 Variances...

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