R Dataset / Package HistData / Michelson
On this Picostat.com 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. Try to load the Michelson data set in R by issuing the following command at the console data("Michelson"). This may 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 library("HistData") followed by data("Michelson"). Perhaps strangley, if R gives you no output after entering a command, it means the command succeeded. If it succeeded you can see the data by typing Michelson at the command-line which should display the entire dataset.
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
The data frame
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
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.
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.
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