R Dataset / Package HistData / Michelson

On this R-data statistics page, you will find information about the Michelson data set which pertains to Michelson's Determinations of the Velocity of Light. The Michelson data set is found in the HistData R package. You can load the Michelson data set in R by issuing the following command at the console data("Michelson"). This will load the data into a variable called Michelson. If R says the Michelson data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data with the library() command. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Michelson R data set. The size of this file is about 415 bytes.

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

data(Michelson)
data(MichelsonSets)

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.

Examples

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")

Dataset imported from https://www.r-project.org.

Attachments: csv, json

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