On this R-data statistics page, you will find information about the MichelsonSets data set which pertains to Michelson's Determinations of the Velocity of Light. The MichelsonSets data set is found in the HistData R package. You can load the MichelsonSets data set in R by issuing the following command at the console data("MichelsonSets"). This will load the data into a variable called MichelsonSets. If R says the MichelsonSets 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. 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 MichelsonSets R data set. The size of this file is about 439 bytes.
Michelson's Determinations of the Velocity of Light
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
Michelson: A data frame with 100 observations on the following variable, given in time order of data collection
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" ...
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.
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
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.
morley for these data in another format
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)
abline(v=734.5, col="red", lwd=2)
text(mean(Michelson$velocity), .004, "mean", srt=90, pos=2)
text(734.5, .004, "true", srt=90, pos=2)# index / time series plot
abline(h=734.5, col="red", lwd=2)
lines(lowess(Michelson$velocity), col="blue", lwd=2)# examine lag=1 differences
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+.05, tm, pch=16, col="blue")
Dataset imported from https://www.r-project.org.