+-------------+-------------------+
| Michelson   | R Documentation   |
+-------------+-------------------+

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.xhtml <http://www.math.uah.edu/stat/data/Michelson.xhtml>`_

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
~~~~~~~~

::

    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")

