# Lecture11B - 05 June 2003 Biostatistics 6650-L11B 1 Todays...

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05 June 2003 Biostatistics 6650--L11B 1

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05 June 2003 Biostatistics 6650--L11B 2 Today’s Schedule ANOVA example contrasts in means Multiple Comparison Procedures general issue “solutions” example controversy
05 June 2003 Biostatistics 6650--L11B 3 ANOVA: testing for normality Shapiro-Wilk W test form can be used to test for departures from a normal distribution Available in JMP(distributions, fit normal, goodness of fit) Ho: Data follow a normal distribution Ha: Data do not follow a normal distribution We hope to find a non-significant p-value, as we do not wish to reject normality. We want a p-value>0.05.

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05 June 2003 Biostatistics 6650--L11B 4 ANOVA: testing for normality 0-0 Distributions cyp1b1 .05 .075 .1 .125 .15 .175 Normal(0.10333,0.04509) Fitted Normal Goodness-of-Fit Test Shapiro-Wilk W Test W Prob<W 0.995883 0.8774 1-1 Distributions cyp1b1 1.55 1.6 1.65 1.7 1.75 1.8 Normal(1.66,0.09) Fitted Normal Goodness-of-Fit Test Shapiro-Wilk W Test W Prob<W 0.999981 0.9916
05 June 2003 Biostatistics 6650--L11B 5 ANOVA: testing for normality Shapiro-Wilk W test, continued Consider other information histogram normal curve applied to histogram mean vs median sample size difficult to reject normality with low n with large n, even relatively minor departures from normality may result in a “significant” p-value

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05 June 2003 Biostatistics 6650--L11B 6 ANOVA: Common Variance Like the t-test, ANOVA is quite robust to this assumption 4 tests in JMP to choose one consider approximate normality of data and skewness If test is significant at 1% level, then what? Use Welch’s ANOVA(in JMP) which does not require equal variances (Milliken and Johnson, 1992)--not too familiar with this do separate t-tests to compare groups(need protection against type I error) transform the data use rank based procedures, coming Note: these concepts apply equally to the two-sample t-test
05 June 2003 Biostatistics 6650--L11B 7 ANOVA: Common Variance JMP common variance tests Bartlett’s test based on geometric average of sample variances relative to overall variance valid only under normality often used, one of first tests developed Levene’s test based on F from ANOVA where Y ij = | x ij - Mean i | nearly as powerful as Bartlett’s for normal data more powerful than Bartlett’s for non-normal data| Brown-Forsythe Test similar to Levene’s, better when data are skewed based on F from ANOVA where Y ij = | x ij - Median i | O’Brien’s test uses F from ANOVA on Y ij , where mean Y ij =sample variances

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05 June 2003 Biostatistics 6650--L11B 8 ANOVA: Common Variance Oneway Analysis of cyp1b1 By male_cyst cyp1b1 0 0.5 1 1.5 2 0/0 0/1 1/0 1/1 male_cyst Tests that the Variances are Equal Level Count Std Dev MeanAbsDif to Mean MeanAbsDif to Median 0/0 3 0.0450925 0.0311111 0.0433333 0/1 3 0.0450925
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## This note was uploaded on 06/17/2011 for the course BME 6650 taught by Professor Multipleinstructors during the Spring '03 term at Mayo Clinic College of Medicine.

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Lecture11B - 05 June 2003 Biostatistics 6650-L11B 1 Todays...

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