# Michelson's Determinations of the Velocity of Light

### Description

The data frame `Michelson`

gives Albert Michelson's measurements of the velocity of light in air,
made from June 5 to July 2, 1879, reported in Michelson (1882).
The given values + 299,000 are Michelson's measurements in km/sec.
The number of cases is 100 and the "true" value on this scale is 734.5.

Stigler (1977) used these data to illustrate properties of robust estimators
with real, historical data. For this purpose, he divided the 100 measurements
into 5 sets of 20 each. These are contained in `MichelsonSets`

.

### Usage

1 2 |

### Format

`Michelson`

: A data frame with 100 observations on the following variable, given in time order of
data collection

`velocity`

a numeric vector

`MichelsonSets`

: A 20 x 5 matrix, with format
int [1:20, 1:5] 850 850 1000 810 960 800 830 830 880 720 ...
- attr(*, "dimnames")=List of 2
..$ : NULL
..$ : chr [1:5] "ds12" "ds13" "ds14" "ds15" ...

### Details

The "true" value is taken to be 734.5, arrived at by taking the "true" speed of light in a vacuum to be 299,792.5 km/sec, and adjusting for the velocity in air.

The data values are recorded in order, and so may also be taken as a time series.

### Source

Kyle Siegrist, "Virtual Laboratories in Probability and Statistics", http://www.math.uah.edu/stat/data/Michelson.html

Stephen M. Stigler (1977), "Do robust estimators work with *real* data?", *Annals of Statistics*, 5, 1055-1098

### References

Michelson, A. A. (1882). "Experimental determination of the velocity of light made at the
United States Naval Academy, Anapolis". *Astronomical Papers*, 1,109-145,
U. S. Nautical Almanac Office.

### See Also

`morley`

for these data in another format

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
data(Michelson)
# density plot (default bandwidth & 0.6 * bw)
plot(density(Michelson$velocity), xlab="Speed of light - 299000 (km/s)",
main="Density plots of Michelson data")
lines(density(Michelson$velocity, adjust=0.6), lty=2)
rug(jitter(Michelson$velocity))
abline(v=mean(Michelson$velocity), col="blue")
abline(v=734.5, col="red", lwd=2)
text(mean(Michelson$velocity), .004, "mean", srt=90, pos=2)
text(734.5, .004, "true", srt=90, pos=2)
# index / time series plot
plot(Michelson$velocity, type="b")
abline(h=734.5, col="red", lwd=2)
lines(lowess(Michelson$velocity), col="blue", lwd=2)
# examine lag=1 differences
plot(diff(Michelson$velocity), type="b")
lines(lowess(diff(Michelson$velocity)), col="blue", lwd=2)
# examine different data sets
boxplot(MichelsonSets, ylab="Velocity of light - 299000 (km/s)", xlab="Data set")
abline(h=734.5, col="red", lwd=2)
# means and trimmed means
(mn <-apply(MichelsonSets, 2, mean))
(tm <- apply(MichelsonSets, 2, mean, trim=.1))
points(1:5, mn)
points(1:5+.05, tm, pch=16, col="blue")
``` |