robustbase: cushny – R documentation

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cushny

Cushny and Peebles Prolongation of Sleep Data

Description

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.

Usage

data(cushny, package="robustbase")

Format

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

Source

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).

References

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.

Examples

data(cushny)

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]] })
stopifnot(all.equal(cushny,
                    sort(d.sleep), tolerance=1e-15))

robustbase

Basic Robust Statistics

v0.93-7

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Peter Rousseeuw [ctb] (Qn and Sn), Christophe Croux [ctb] (Qn and Sn), Valentin Todorov [aut] (most robust Cov), Andreas Ruckstuhl [aut] (nlrob, anova, glmrob), Matias Salibian-Barrera [aut] (lmrob orig.), Tobias Verbeke [ctb, fnd] (mc, adjbox), Manuel Koller [aut] (mc, lmrob, psi-func.), Eduardo L. T. Conceicao [aut] (MM-, tau-, CM-, and MTL- nlrob), Maria Anna di Palma [ctb] (initial version of Comedian)

Initial release

2021-01-04