Chapter 12--Multisample Inference

Microarray chapter 12 multisample inference stat 491

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Unformatted text preview: p(1) ≤ p(2) ≤ · · · ≤ p(m) . Let J be the largest index for which p(j ) ≤ j × α. m The comparisons corresponding to the ranks (1), · · · , (J ) are declared significant. This procedure controls FDR at level α. The adjusted p-value for the j th largest contrast is (m/j )p(j ) . Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: The Blood Pressure Data #fdr and bonferroni for l_1,l_2 and l_3 summary(mc,test=adjusted(type=c("fdr"))) summary(mc,test=adjusted(type=c("fdr"))) #fdr all-pairwise comparison apc<-glht(A,linfct=mcp(f="Tukey")) summary(apc,test=adjusted(type=c("bonferroni"))) summary(apc,test=adjusted(type=c("fdr"))) Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: cDNA Microarray Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: cDNA Microarray Experiment Data consists of gene expression profiles obtained on a collection of 25 prostate tissue samples, comprised of 16 prostate cancers and 9 benign prostatic hyperplasia (enlargement of prostate) specimens. Goal is to identify differentially-expressed genes. Total 5854 genes. We have p-values for each gene (total 5854 p-values). The p-values were adjusted for multiplicity using Benjamini-Hochberg’s and Bonferroni’s method. In R, adjustment is done by p.adjust(p_value,method="fdr") Bonferroni declared only 47 genes differentially expressed. Benjamini-Hochberg’s procedure declared 652 genes as differentially expressed. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example: Plot of adjusted and unadjusted p values Bonferroni Benjamini−Hochburg 6000 6000 5000 qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqq qqqqqqqqqqqqqqqqqqqqqqqqqqq qqqq qq qq qq qqqqq qqqqqq qq q qqqqqq qq q qqqq q qq qq qqq q qqqqq q q q qqqq q q q q qq 5000 q q 6000 5000 1.0 Unadjusted q q q 0.8 Bonferroni 0.4 q q q q q q q q 0.2 0.4 0.6 p 0.8 1.0 0.2 2000 0 0.0 1000 2000 1000 0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 p Chapter 12: Multisample Inference q q q q q q q q q 0.6 4000 Frequency 3000 4000 Frequency 3000 3000 2000 1000 0 Frequency 4000 q q q q q q q q q q q 0.0 0.2 0.4 0.6 0.8 1.0 p Stat 491: Biostatistics q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0.00 0.02 0.04 Benjamini−Hochburg 0.06 Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Kruskal-Wallis Test In ANOVA, we assume the data to have come from normal distributions. This assumption may be violated. For example, the data could be ordinal. The null hypothesis is that the distributions generating the data are the same. This hypothesis means, for example in treatment comparisons, the treatments are equally effective. Combine the samples and rank them from 1 to n. Let k Ri2 12 H= ...
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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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