Chapter 12--Multisample Inference

# 05215 fisher confintmccalphaqt1 005615 bonferroni

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Unformatted text preview: VA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: R Code library(multcomp) #need to download and install the package BP&lt;-c(27, 26, 21, 26, 19, 13, 15, 16,15, 10, 10, 11,22, 15, 21, 18,20, 18, 17, 16) T&lt;-rep(c(&quot;S&quot;,&quot;AL&quot;,&quot;AH&quot;,&quot;BL&quot;,&quot;BH&quot;),each=4) Tx&lt;-factor(T) A&lt;-aov(BP~Tx) summary(A) contr&lt;-rbind(&quot;AL-AH&quot;=c(0,-1,1,0,0), &quot;BL-BH&quot;=c(0,0,0,-1,1), &quot;A-B&quot;=c(0,1/2,1/2,-1/2,-1/2)) mc&lt;-glht(A,linfct=mcp(f=contr)) summary(mc,test=adjusted(type=c(&quot;none&quot;))) #Fisher summary(mc,test=adjusted(type=c(&quot;bonferroni&quot;))) confint(mc,calpha=qt(1-0.05/2,15)) #Fisher confint(mc,calpha=qt(1-0.05/6,15)) #Bonferroni Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example Cont’d... Surprised by the mean drop in the blood pressure for the two treatments involving drug A, the investigator decided to see whether the data provides evidence (at α = 0.05) that the BP reductions for S+A and S are diﬀerent. ˆ4 = (1/2)(¯AL + yAH ) − yS = −11.375 y ¯ ¯ and ˆ V ( ˆ4 ) = ( 1 )2 ( 1 )2 (−1)2 2 +2 + 4 4 4 Chapter 12: Multisample Inference × 6.433 = 2.412. Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example Cont’d... Scheﬀe’s Method S= ˆ (k − 1)F1−α,k −1,n−k V ( ˆ4 ) = √ 4 × 3.06 × 2.412 = 5.430. Since | ˆ4 | &gt; 5.430, we conclude that ˆ4 is signiﬁcant. Assuming the decision to test the signiﬁcance of ˆ4 was made prior to looking at the data, Fisher’s method rejection cut-oﬀ point is t1−α/2,n−k ˆ V ( ˆ4 ) = 2.131 × 1.553 = 3.311. Although, both method declare ˆ4 signiﬁcant, Scheﬀe’s cut-oﬀ point is bigger than that of Fisher’s. Hence, Fisher’s method is more likely to declare signiﬁcance. Therefore, it should not be used for post-hoc comparisons. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA All Pairwise Comparisons Used in experiments that are exploratory in nature. Give k treatments, there are k (k − 1)/2 possible pairwise comparisons. So if k = 6, there are 15 possible pairwise comparisons. Needless to say, Fisher’s, Bonferroni and Scheﬀe Method discussed previously can be used. Fisher’s will likely declare many false signiﬁcance. Bonferroni and Scheﬀe will tend to be too conservative. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Strategy for All Pairwise Comparison (k=4) 1 Arrange the sample means from the smallest to the largest y(1) , ¯ 2 y(2) , ¯ y(3) , ¯ y(4) ¯ with the corresponding sample sizes n(1) , n(2) , n(3) and n(4) . Determine the order in which the diﬀerence will be tested, (4, 1), (4, 2), (4, 3), (3, 1), (3, 2), (2, 1) 3 The diﬀerence y(i ) − y(j ) is declared signiﬁcant if ¯ ¯ y(i ) − y(j ) &gt; LSDij ¯ ¯ 4 Group toget...
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## This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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