Software and Example Code for Bootstrap Confidence Intervals for Means and Differences in Means

The following uses the simple nonparametric bootstrap percentile approach in R. To obtain 0.95 confidence intervals for a single mean use

library(Hmisc)
smean.cl.boot(x, B=2000)
To get the confidence interval for the difference in two means, say between treatments A and B:

bootdif <- function(y, g) {
 g <- as.factor(g)
 a <- attr(smean.cl.boot(y[g==levels(g)[1]], B=2000, reps=TRUE),'reps')
 b <- attr(smean.cl.boot(y[g==levels(g)[2]], B=2000, reps=TRUE),'reps')
 meandif <- diff(tapply(y, g, mean, na.rm=TRUE))
 a.b <- quantile(b-a, c(.025,.975))
 res <- c(meandif, a.b)
 names(res) <- c('Mean Difference','.025','.975')
 res
}
bootdif(blood.pressure, treatment)
To show bootstrap nonparametric CLs for 3 group means and for pairwise differences on the same graph:

set.seed(1)
group <- sample(c('a','b','d'), 200, TRUE)
y     <- runif(200) + .25*(group=='b') + .5*(group=='d')
cla <- smean.cl.boot(y[group=='a'],reps=TRUE)
a   <- attr(cla,'reps')
clb <- smean.cl.boot(y[group=='b'],reps=TRUE)
b   <- attr(clb,'reps')
cld <- smean.cl.boot(y[group=='d'],reps=TRUE)
d   <- attr(cld,'reps')
a.b <- quantile(a-b,c(.025,.975))
a.d <- quantile(a-d,c(.025,.975))
b.d <- quantile(b-d,c(.025,.975))
errbar(c('a','b','d','a - b','a - d','b - d'),
       c(cla[1], clb[1], cld[1],
       cla[1]-clb[1], cla[1]-cld[1], clb[1]-cld[1]),
       c(cla[3], clb[3], cld[3], a.b[2], a.d[2], b.d[2]),
       c(cla[2], clb[2], cld[2], a.b[1], a.d[1],b.d[1]),
       Type=c(1,1,1,2,2,2))

Bootstrap confidence intervals for means and differences in means

bootdiffs.png
Topic attachments
I Attachment Action Size Date Who Comment
bootdiffs.pngpng bootdiffs.png manage 2.2 K 09 Mar 2007 - 11:12 FrankHarrell Bootstrap confidence intervals for means and differences in means
Topic revision: r1 - 09 Mar 2007, FrankHarrell
 

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