Test robustness of one way anova when independence assumption is violated
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As the title, I want to test the robustness of one way anova when the independence assumption is violated. The scenario is there is correlation between different subgroups. I used mvrnorm to generate correlated datasets, and do the simulation for 1000 times to calculate power of anova for each correlation from 0.1 to 0.9.
However it seems for each iteration the p value of anova stays constant. I hope to know the whether it is because of the way I used to generate correlated subsets is inappropriate or because of something else?? I find in fact the p value does change, but very very slightly... I expect to see when correlation increases, the power will decrease??, but in my case the power is either 1 or 0... (I have put sd for each group to be 1 for simplicity).
myfun3 <- function(index, cor, samplesize, mean1, mean2, mean3){
library(MASS)
data = mvrnorm(n=samplesize, mu=c(mean1, mean2, mean3),
Sigma=matrix(c(1, rep(cor, 3), 1, rep(cor, 3), 1), 3, 3), empirical=TRUE)
newdat<- data.frame(data)
library(tidyr)
newdat_long <- gather(newdat, group, y, X1:X3, factor_key = TRUE)
aov_result <- summary(aov(y ~ group, newdat_long))[[1]][["Pr(>F)"]][[1]]
ks_result <- kruskal.test(y ~ group, newdat_long)$p.value
return(list(aov_result, ks_result))
}
cal_power_cor <- function(iteration = 1000, samplesize=30, cor, mean1 = 10, mean2=10.5, mean3=10.8){
result_list <- lapply(1:iteration, myfun3, samplesize = samplesize, cor = cor, mean1 = mean1, mean2 = mean2,
mean3 = mean3)
result <-data.frame(matrix(unlist(result_list), ncol = 2, byrow = T))
colnames(result)<- c("anova", "kruskal")
power_aov <- sum(result$anova<0.05)/1000
power_kruskal <- sum(result$kruskal<0.05)/1000
return(list("power_aov" = power_aov, "power_kruskal" = power_kruskal))
}
cal_power_cor(cor = 0.2)
cal_power_cor(cor = 0.5)
cal_power_cor(cor = 0.9)
r anova robustness
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
add a comment |
As the title, I want to test the robustness of one way anova when the independence assumption is violated. The scenario is there is correlation between different subgroups. I used mvrnorm to generate correlated datasets, and do the simulation for 1000 times to calculate power of anova for each correlation from 0.1 to 0.9.
However it seems for each iteration the p value of anova stays constant. I hope to know the whether it is because of the way I used to generate correlated subsets is inappropriate or because of something else?? I find in fact the p value does change, but very very slightly... I expect to see when correlation increases, the power will decrease??, but in my case the power is either 1 or 0... (I have put sd for each group to be 1 for simplicity).
myfun3 <- function(index, cor, samplesize, mean1, mean2, mean3){
library(MASS)
data = mvrnorm(n=samplesize, mu=c(mean1, mean2, mean3),
Sigma=matrix(c(1, rep(cor, 3), 1, rep(cor, 3), 1), 3, 3), empirical=TRUE)
newdat<- data.frame(data)
library(tidyr)
newdat_long <- gather(newdat, group, y, X1:X3, factor_key = TRUE)
aov_result <- summary(aov(y ~ group, newdat_long))[[1]][["Pr(>F)"]][[1]]
ks_result <- kruskal.test(y ~ group, newdat_long)$p.value
return(list(aov_result, ks_result))
}
cal_power_cor <- function(iteration = 1000, samplesize=30, cor, mean1 = 10, mean2=10.5, mean3=10.8){
result_list <- lapply(1:iteration, myfun3, samplesize = samplesize, cor = cor, mean1 = mean1, mean2 = mean2,
mean3 = mean3)
result <-data.frame(matrix(unlist(result_list), ncol = 2, byrow = T))
colnames(result)<- c("anova", "kruskal")
power_aov <- sum(result$anova<0.05)/1000
power_kruskal <- sum(result$kruskal<0.05)/1000
return(list("power_aov" = power_aov, "power_kruskal" = power_kruskal))
}
cal_power_cor(cor = 0.2)
cal_power_cor(cor = 0.5)
cal_power_cor(cor = 0.9)
r anova robustness
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
add a comment |
As the title, I want to test the robustness of one way anova when the independence assumption is violated. The scenario is there is correlation between different subgroups. I used mvrnorm to generate correlated datasets, and do the simulation for 1000 times to calculate power of anova for each correlation from 0.1 to 0.9.
However it seems for each iteration the p value of anova stays constant. I hope to know the whether it is because of the way I used to generate correlated subsets is inappropriate or because of something else?? I find in fact the p value does change, but very very slightly... I expect to see when correlation increases, the power will decrease??, but in my case the power is either 1 or 0... (I have put sd for each group to be 1 for simplicity).
myfun3 <- function(index, cor, samplesize, mean1, mean2, mean3){
library(MASS)
data = mvrnorm(n=samplesize, mu=c(mean1, mean2, mean3),
Sigma=matrix(c(1, rep(cor, 3), 1, rep(cor, 3), 1), 3, 3), empirical=TRUE)
newdat<- data.frame(data)
library(tidyr)
newdat_long <- gather(newdat, group, y, X1:X3, factor_key = TRUE)
aov_result <- summary(aov(y ~ group, newdat_long))[[1]][["Pr(>F)"]][[1]]
ks_result <- kruskal.test(y ~ group, newdat_long)$p.value
return(list(aov_result, ks_result))
}
cal_power_cor <- function(iteration = 1000, samplesize=30, cor, mean1 = 10, mean2=10.5, mean3=10.8){
result_list <- lapply(1:iteration, myfun3, samplesize = samplesize, cor = cor, mean1 = mean1, mean2 = mean2,
mean3 = mean3)
result <-data.frame(matrix(unlist(result_list), ncol = 2, byrow = T))
colnames(result)<- c("anova", "kruskal")
power_aov <- sum(result$anova<0.05)/1000
power_kruskal <- sum(result$kruskal<0.05)/1000
return(list("power_aov" = power_aov, "power_kruskal" = power_kruskal))
}
cal_power_cor(cor = 0.2)
cal_power_cor(cor = 0.5)
cal_power_cor(cor = 0.9)
r anova robustness
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
As the title, I want to test the robustness of one way anova when the independence assumption is violated. The scenario is there is correlation between different subgroups. I used mvrnorm to generate correlated datasets, and do the simulation for 1000 times to calculate power of anova for each correlation from 0.1 to 0.9.
However it seems for each iteration the p value of anova stays constant. I hope to know the whether it is because of the way I used to generate correlated subsets is inappropriate or because of something else?? I find in fact the p value does change, but very very slightly... I expect to see when correlation increases, the power will decrease??, but in my case the power is either 1 or 0... (I have put sd for each group to be 1 for simplicity).
myfun3 <- function(index, cor, samplesize, mean1, mean2, mean3){
library(MASS)
data = mvrnorm(n=samplesize, mu=c(mean1, mean2, mean3),
Sigma=matrix(c(1, rep(cor, 3), 1, rep(cor, 3), 1), 3, 3), empirical=TRUE)
newdat<- data.frame(data)
library(tidyr)
newdat_long <- gather(newdat, group, y, X1:X3, factor_key = TRUE)
aov_result <- summary(aov(y ~ group, newdat_long))[[1]][["Pr(>F)"]][[1]]
ks_result <- kruskal.test(y ~ group, newdat_long)$p.value
return(list(aov_result, ks_result))
}
cal_power_cor <- function(iteration = 1000, samplesize=30, cor, mean1 = 10, mean2=10.5, mean3=10.8){
result_list <- lapply(1:iteration, myfun3, samplesize = samplesize, cor = cor, mean1 = mean1, mean2 = mean2,
mean3 = mean3)
result <-data.frame(matrix(unlist(result_list), ncol = 2, byrow = T))
colnames(result)<- c("anova", "kruskal")
power_aov <- sum(result$anova<0.05)/1000
power_kruskal <- sum(result$kruskal<0.05)/1000
return(list("power_aov" = power_aov, "power_kruskal" = power_kruskal))
}
cal_power_cor(cor = 0.2)
cal_power_cor(cor = 0.5)
cal_power_cor(cor = 0.9)
r anova robustness
r anova robustness
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
edited Nov 16 '18 at 20:54
Teng Li
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
asked Nov 16 '18 at 20:49
Teng LiTeng Li
84
84
add a comment |
add a comment |
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