cushny: Cushny and Peebles Prolongation of Sleep Data

cushnyR Documentation

Cushny and Peebles Prolongation of Sleep Data


The original data set was bivariate and recorded for ten subjects the prolongation of sleep caused by two different drugs. These data were used by Student as the first illustration of the paired t-test which only needs the differences of the two measurements. These differences are the values of cushny.


data(cushny, package="robustbase")


numeric vector, sorted increasingly:
0 0.8 1 1.2 1.3 1.3 1.4 1.8 2.4 4.6


Cushny, A.R. and Peebles, A.R. (1905) The action of optical isomers. II. Hyoscines. J. Physiol. 32, 501–510.

These data were used by Student(1908) as the first illustration of the paired t-test, see also sleep; then cited by Fisher (1925) and thereforth copied in numerous books as an example of a normally distributed sample, see, e.g., Anderson (1958).


Student (1908) The probable error of a mean. Biometrika 6, 1–25.

Fisher, R.A. (1925) Statistical Methods for Research Workers; Oliver & Boyd, Edinburgh.

Anderson, T.W. (1958) An Introduction to Multivariate Statistical Analysis; Wiley, N.Y.

Hampel, F., Ronchetti, E., Rousseeuw, P. and Stahel, W. (1986) Robust Statistics: The Approach Based on Influence Functions; Wiley, N.Y.



plot(cushny,  rep(0, 10), pch = 3, cex = 3,
     ylab = "", yaxt = "n")
plot(jitter(cushny),  rep(0, 10), pch = 3, cex = 2,
     main = "'cushny' data (n= 10)", ylab = "", yaxt = "n")
abline(h=0, col="gray", lty=3)
myPt <- function(m, lwd = 2, ..., e = 1.5*par("cxy")[2])
  segments(m, +e, m, -e, lwd = lwd, ...)
myPt(  mean(cushny), col = "pink3")
myPt(median(cushny), col = "light blue")
legend("topright", c("mean", "median"), lwd = 2,
       col = c("pink3", "light blue"), inset = .01)

## The 'sleep' data from the standard 'datasets' package:
d.sleep <- local({ gr <- with(datasets::sleep, split(extra, group))
                   gr[[2]] - gr[[1]] })
                    sort(d.sleep), tolerance=1e-15))

robustbase documentation built on July 10, 2023, 2:01 a.m.