Chapter 12--Multisample Inference

0520 kk 120 chapter 12 multisample inference stat 491

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Unformatted text preview: her the means that are not significantly different. The groups may overlap. They are identified by underlining the ordered means belonging to the same groups. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Methods 1. Fisher (only PCER) LSDij (F ) = t1−α/2,n−k 1 1 + n(i ) n(j ) 2 sW 2. Bonferroni (EWER) LSDij (B ) = t1− k (kα 1) ,n−k − 1 1 + n(i ) n(j ) 2 sW 3. Scheffe (EWER) LSDij (S ) = (k − 1)F1−α,k −1,n−k Chapter 12: Multisample Inference 1 1 + n(i ) n(j ) Stat 491: Biostatistics 2 sW Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: The BP Data apc<-glht(A,linfct=mcp(f="Tukey")) summary(apc,test=adjusted(type=c("bonferroni"))) confint(apc,c_alpha=(1-0.05/20)) #k(k-1)=20 Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: Insectology In a research to investigate the attractiveness of five different colors to insects, the number of cereal leaf beetles trapped when six boards of each of the five colors were placed in a field of oats were recorded. The following summary statistics were computed. Color ni yi . ¯ Yellow 6 49.2 Orange 6 34.9 Red 6 26.4 Blue 6 17.2 White 6 15.0 2 = 63.298. sW Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example Cont’d ... Pair Y vs W Y vs B Y vs R Y vs O O vs W B vs O O vs R R vs W R vs B B vs W Diff 34.2 32 22.8 14.3 19.9 17.7 8.5 11.4 9.2 2.2 F 9.46 9.46 9.46 9.46 9.46 9.46 9.46 9.46 9.46 9.46 B 14.139 14.139 14.139 14.139 14.139 14.139 14.139 14.139 14.139 14.139 Chapter 12: Multisample Inference S 15.259 15.259 15.259 15.259 15.259 15.259 15.259 15.259 15.259 15.259 Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Remarks The cut off points for different pairwise comparisons would be different for each of the method if the sample sizes were not equal. We want a procedure that, ideally, not only controls EWER but also has high power to detect true significance (has the smallest LSD). Which of Bonferroni or Scheffe method should we use? Fisher is not generally recommended because it does not control EWER. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA False Discovery Rate (FDR) Bonferroni’s and Schefe procedures control EWER but they tend to be conservative when m and k are large. Controlling EWER, in general, may not be practical for large-scale inference (large k and m). For large scale inference, EWER results in conservative inferential procedures. An error rate which has gained popularity in genetic studies is the so-called False Discovery Rate. FDR is defined as the expected proportion of falsely declared significant among all declared significant, FDR = E V R . In general, FDR ≤ αE . Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Benjamini-Hochberg Procedure We first compute p -value for each comparison using a method that controls (PCER) such as Fisher’s procedure. Order the p -values from the smallest to the largest...
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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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