cushny | R Documentation |

## 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))
```