16d-Anova_PostANOVACalc

16d-Anova_PostANOVACalc - EXST7015 : Statistical Techniques...

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EXST7015 : Statistical Techniques II Geaghan ANOVA – Treatment Arrangements Post-hoc description Page 1 16f-Anova-PostANOVA Usual Analysis of variance procedure 1) H 0 : µ 1 = µ 2 = µ 3 = µ 4 = µ 5 = µ 2) H 1 : some µ i is different 3) a) Assume that the observations are normally distributed about each mean, or that the residuals (i.e. deviations) are normally distributed. b) Assume that the observations are independent c) Assume that the variances are homogeneous 4) Set the level of type I error. Usually α = 0.05 5) Determine the critical value. The test is in ANOVA is a one tailed F test. 6) Obtain data and evaluate. 7) Conclusions Descriptions of post-hoc tests Post-hoc or Post-ANOVA tests ! Once you have found out some treatment(s) are “different”, how do you determine which one(s) are different? If we had done a t-test on the individual pairs of treatments, the test would have been done as t YY S nn MSE p = + = + 12 2 11 () . If the difference between was large enough, the t value would have been greater than the t critical and we would conclude that there was a significant difference between the means. Since we know the value of t critical we could figure out how large a difference is needed for significance for any particular values of MSE, n 1 and n 2 . We do this by replacing t with t critical and solving for . t S p MSE = + = + 2 1 1 1 2 1 1 1 2 , so tM S E critical += or YY t S criticalYY −= This value is the exact width of an interval which would give a t-test equal to t critical . Any larger values would be “significant” and any smaller values would not. This is called the “Least Significant Difference”. LSD t S = This least significant difference calculation can be used to either do pairwise tests on observed differences or to place a confidence interval on observed differences. The LSD can be done in SAS in one of two ways. The MEANS statement produces a range test (LINES option) or confidence intervals (CLDIFF option), while the LSMEANS statement gives pairwise comparisons.
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EXST7015 : Statistical Techniques II Geaghan ANOVA – Treatment Arrangements Post-hoc description Page 2 16f-Anova-PostANOVA The LSD has an α probability of error on each and every test.
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This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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16d-Anova_PostANOVACalc - EXST7015 : Statistical Techniques...

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