Power Analysis in One-Way ANOVA: R Code and Interpretation, Assignments of Statistics

Download Power Analysis in One-Way ANOVA: R Code and Interpretation and more Assignments Statistics in PDF only on Docsity! 22s:158/165 Homework 7 solutions 1. (Exercise 7.2) Using R, > means=c(10,11,11) > sig.2=4 > ## Get non-centrality parameter: > alphas=means-mean(means) > ncp=6*sum(alphas^2)/sig.2 > > between.variance=sum((alphas)^2)/2 > power.anova.test(groups=3,between.var=between.variance,within.var=sig.2, sig.level=0.05,power=0.90) Balanced one-way analysis of variance power calculation groups = 3 n = 76.93183 between.var = 0.3333333 within.var = 4 sig.level = 0.05 power = 0.9 NOTE: n is number in each group So, the sample size is n=77 to get a power of at least 0.90. 2. (Exercise 7.3) > g=4 > sum.alphas.2=6 ## This is the sum of the squared treatment effects. > sig.2=3 > n=4 > N=n*g > > ## Get noncentrality parameter: > ncp=n*sum.alphas.2/sig.2 > ncp [1] 8 > > #significance threshold computed under H0 true: > cutoff=qf(0.99,g-1,N-g) > cutoff [1] 5.952545 1 > ## Find the power under HA true: > power=pf(cutoff,g-1,N-g,ncp,lower.tail=FALSE) > power [1] 0.2260942 So, the power is 0.23. 3. (Exercise 7.4) 1. FALSE. The probability of rejecting the null hypothesis when the null is false (and the alternative is true) IS the power, and this is 0.85. 2. FALSE. The probability of failing to reject H0 when H0 is true, is the probability of accepting H0 when it is true, and this is α, which is 0.05. 4. (Problem 7.2) > g=3 > means=c(45,32,60) > sig.2=36 > ## Get between group variance: > alphas=means-mean(means) > between.variance=sum((alphas)^2)/(g-1) > power.anova.test(groups=g,between.var=between.variance,within.var=sig.2, sig.level=0.01,power=0.95) Balanced one-way analysis of variance power calculation groups = 3 n = 3.674063 between.var = 196.3333 within.var = 36 sig.level = 0.01 power = 0.95 NOTE: n is number in each group So, the sample size is n=4 to get a power of at least 0.95. 2