bootstrap CI of the difference between 2 Cramer's V

Dear Daniel,
Dear R-experts,

I really thank you a lot Daniel. Nobody had answered to me offline. So, thanks.
I have tried in the same vein for the Goodman-Kruskal gamma for ordinal data. There is an error message at the end of the code. Thanks for your help.


##############################
library(ryouready)
library(boot)

shopping1<-c("tr?s important","important","pas important","pas important","important","tr?s important","important","pas important","tr?s important","tr?s important","important","pas important","pas important","important","tr?s important","tr?s important","important","pas important","pas important","important","tr?s important","tr?s important","important","pas important","pas important","important","tr?s important","tr?s important","important","pas important","pas important","important","tr?s important","tr?s important","important","pas important","pas important","important","tr?s important","important")

statut1<-c("riche","pas riche","moyennement riche","moyennement riche","riche","pas riche","moyennement riche","moyennement riche","riche","pas riche","moyennement riche","riche","pas riche","pas riche","riche","moyennement riche","riche","pas riche","pas riche","pas riche","riche","riche","moyennement riche","riche","riche","moyennement riche","moyennement riche","moyennement riche","pas riche","pas riche","riche","pas riche","riche","pas riche","riche","moyennement riche","riche","pas riche","moyennement riche","riche")

shopping2<-c("important","pas important","tr?s important","tr?s important","important","tr?s important","pas important","important","pas important","tr?s important","important","important","important","important","pas important","tr?s important","tr?s important","important","pas important","tr?s important","pas important","tr?s important","pas important","tr?s important","important","tr?s important","important","pas important","pas important","important","pas important","tr?s important","pas important","pas important","important","important","tr?s important","tr?s important","pas important","pas important")

statut2<-c("moyennement riche","pas riche","riche","moyennement riche","moyennement riche","moyennement riche","pas riche","riche","riche","pas riche","moyennement riche","riche","riche","riche","riche","riche","pas riche","moyennement riche","moyennement riche","pas riche","moyennement riche","pas riche","pas riche","pas riche","moyennement riche","riche","moyennement riche","riche","pas riche","riche","moyennement riche","blue","moyennement riche","pas riche","pas riche","riche","riche","pas riche","pas riche","pas riche")

f1 <- data.frame(shopping=shopping1,statut=statut1,group='grp1')
f2 <- data.frame(shopping=shopping2,statut=statut2,group='grp2')
f3 <- rbind(f1,f2)

G <- function(x, index) {
?? 
# calculate goodman for group 1 bootstrap sample
?? g1 <-x[index,][x[,3]=='grp1',]
?? goodman_g1 <- cor(data[index,][1,2])
??
?# calculate goodman for group 2 bootstrap sample
?? g2 <-x[index,][x[,3]=='grp2',]
?? goodman_g2 <- cor(data[index,][3,4])
??
?# calculate difference
?? goodman_g1-goodman_g2
?? }
?

# use strata parameter in function boot to resample within each group
results <- boot(data=f3,statistic=G, strata=as.factor(f3$group),R=2000)

results
boot.ci(results)
##############################



Le samedi 4 juin 2022 ? 09:31:36 UTC+2, Daniel Nordlund <djnordlund at gmail.com> a ?crit :

Dear R-experts,

While comparing groups, it is better to assess confidence intervals of those differences rather than comparing confidence intervals for each group.
I am trying to calculate the CIs of the difference between the two Cramer's V and not the CI to the estimate of each group?s Cramer's V.

Here below my toy R example. There are error messages. Any help would be highly appreciated.

##############################
library(questionr)
library(boot)

gender1<-c("M","F","F","F","M","M","F","F","F","M","M","F","M","M","F","M","M","F","M","F","F","F","M","M","M","F","F","M","M","M","F","M","F","F","F","M","M","F","M","F")
color1<-c("blue","green","black","black","green","green","blue","blue","green","black","blue","green","blue","black","black","blue","green","blue","green","black","blue","blue","black","black","green","green","blue","green","black","green","blue","black","black","blue","green","green","green","blue","blue","black")

gender2<-c("F","F","F","M","M","F","M","M","M","F","F","M","F","M","F","F","M","M","M","F","M","M","M","F","F","F","M","M","M","F","M","M","M","F","F","F","M","F","F","F")
color2<-c("green","blue","black","blue","blue","blue","green","blue","green","black","blue","black","blue","blue","black","blue","blue","green","blue","black","blue","blue","black","black","green","blue","black","green","blue","green","black","blue","black","blue","green","blue","green","green","blue","black")

f1=data.frame(gender1,color1)
tab1<-table(gender1,color1)
e1<-cramer.v(tab1)

f2=data.frame(gender2,color2)
tab2<-table(gender2,color2)
e2<-cramer.v(tab2)

f3<-data.frame(e1-e2)

cramerdiff=function(x,w){
y<-tapply(x[w,1], x[w,2],cramer.v)
y[1]-y[2]
}

results<-boot(data=f3,statistic=cramerdiff,R=2000)
results

boot.ci(results,type="all")
##############################

? 

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and provide commented, minimal, self-contained, reproducible code.

I don't know if someone responded offline, but if not, there are a 
couple of problems with your code. ? First, the f3 dataframe is not what 
you think it is.? Second, your cramerdiff function isn't going to 
produce the results that you want.

I would put your data into a single dataframe with a variable 
designating which group data came from.? Then use that variable as the
strata variable in the boot function to resample within groups.? So 
something like this:

f1 <- data.frame(gender=gender1,color=color1,group='grp1')
f2 <- data.frame(gender=gender2,color=color2,group='grp2')
f3 <- rbind(f1,f2)

cramerdiff <- function(x, ndx) {
?? # calculate cramer.v for group 1 bootstrap sample
?? g1 <-x[ndx,][x[,3]=='grp1',]
?? cramer_g1 <- cramer.v(table(g1[,1:2]))
?? # calculate cramer.v for group 2 bootstrap sample
?? g2 <-x[ndx,][x[,3]=='grp2',]
?? cramer_g2 <- cramer.v(table(g2[,1:2]))
?? # calculate difference
?? cramer_g1-cramer_g2
?? }
# use strata parameter in function boot to resample within each group
results <- boot(data=f3,statistic=cramerdiff, 
strata=as.factor(f3$group),R=2000)

results
boot.ci(results)



Hope this is helpful,

Dan

-- 
Daniel Nordlund
Port Townsend, WA? USA

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