Chapter 12--Multisample Inference

# In particular topical application of arachidonic acid

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Unformatted text preview: 3(n + 1) n(n + 1) ni i =1 where Ri is the sum of ranks of observations in the i th group. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Kruskal-Wallis Test If there are no ties we reject H0 if H &gt; χ2 −1,1−α and the k p-value is computed as p−value = P (χ2 −1 &gt; Hcomputed ). k When there are ties, we deﬁne H∗ = H/ 1 − g 3 i =1 (ti − ti ) n3 − n . Then we reject H0 if H ∗ &gt; χ2 −1 and the p-value is computed k as ∗ p−value = P (χ2 −1 &gt; Hcomputed ). k The Kruskal-Wallis test should be used only if the smallest sample size is at least 5. In R, the Kruskal-Wallis test may be done using kruskal.test(formula, data) Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Example:Opthalmology Arachidonic acid is well known to have an eﬀect on ocular metabolism. In particular, topical application of arachidonic acid has caused lid closure, itching and ocular discharge, among other eﬀects. A study was conducted to compare the anti-inﬂammatory eﬀects of four diﬀerent drugs in albino rabbits after administration of arachidonic acid. Six rabbits were studied in each group. Diﬀerent rabbits were used in each of the four groups. For each animal in a group, one of the four drugs was administered to one eye and a saline solution was administered to the other eye. Ten minutes later arachidonic acid (Sodium arachidonate) was administered to both eyes. Both eyes were evaluated every 15 minutes thereafter for lid closure. At each assessment the lids of both eyes were examined and a lid-closure score from 0 to 3 was determined, where 0 = eye completely open, 3 = eye completely closed, and 1,2= intermediate states. Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA The measure of eﬀectiveness (X) is the change in lid-closure (from baseline to follow-up) in the treated eye minus the change in lid-closure score in the saline eye. A high value for X is indicative of an eﬀective drug. The results, after 15 minutes of follow-up, are presented in Table below. Indomethacin +2 +3 +3 +3 +3 0 Aspirin +1 +3 +1 +2 +2 +3 Chapter 12: Multisample Inference Piroxicam +3 +1 +2 +1 +3 +3 BW755C +1 0 0 0 0 -1 Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA All-Pairwise Comparisons The i th and j th treatments are declared diﬀerent if, reject H0 if |Ri − Rj | &gt; z1− k (α ) k 1 n(n + 1) 12 1 1 + . ni nj The above procedure does Bonferroni adjustment for multiplicity. Example: Do all pairwise comparisons for the Ophthalmology example. In R, library(pgirmess) #needs to be installed kruskalmc(x,g,probs=0.05) Chapter 12: Multisample Inference Stat 491: Biostatistics Analysis of Variance (ANOVA) Multiple Comparisons The Kruskal-Wallis Test Two-Way ANOVA Assignment of Treatments to Experimental Units The ANOVA we considered previously is know spe...
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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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