Michelson Speed of Light Data

Description

A classical data of Michelson (but not this one with Morley) on measurements done in 1879 on the speed of light. The data consists of five experiments, each consisting of 20 consecutive ‘runs’. The response is the speed of light measurement, suitably coded (km/sec, with 299000 subtracted).

Usage

morley

Format

A data frame with 100 observations on the following 3 variables.

Expt

The experiment number, from 1 to 5.

Run

The run number within each experiment.

Speed

Speed-of-light measurement.

Details

The data is here viewed as a randomized block experiment with ‘experiment’ and ‘run’ as the factors. ‘run’ may also be considered a quantitative variate to account for linear (or polynomial) changes in the measurement over the course of a single experiment.

Note

This is the same dataset as michelson in package MASS.

Source

A. J. Weekes (1986) A Genstat Primer. London: Edward Arnold.

S. M. Stigler (1977) Do robust estimators work with real data? Annals of Statistics 5, 1055–1098. (See Table 6.)

A. A. Michelson (1882) Experimental determination of the velocity of light made at the United States Naval Academy, Annapolis. Astronomic Papers 1 135–8. U.S. Nautical Almanac Office. (See Table 24.)

Examples

require(stats); require(graphics)
michelson <- transform(morley,
                       Expt = factor(Expt), Run = factor(Run))
xtabs(~ Expt + Run, data = michelson)  # 5 x 20 balanced (two-way)
plot(Speed ~ Expt, data = michelson,
     main = "Speed of Light Data", xlab = "Experiment No.")
fm <- aov(Speed ~ Run + Expt, data = michelson)
summary(fm)
fm0 <- update(fm, . ~ . - Run)
anova(fm0, fm)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
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> library(datasets)
> png(filename="/home/ddbj/snapshot/RGM3/R_rel/result/datasets/morley.Rd_%03d_medium.png", width=480, height=480)
> ### Name: morley
> ### Title: Michelson Speed of Light Data
> ### Aliases: morley
> ### Keywords: datasets
> 
> ### ** Examples
> 
> require(stats); require(graphics)
> michelson <- transform(morley,
+                        Expt = factor(Expt), Run = factor(Run))
> xtabs(~ Expt + Run, data = michelson)  # 5 x 20 balanced (two-way)
    Run
Expt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
   1 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1
   2 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1
   3 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1
   4 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1
   5 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1
> plot(Speed ~ Expt, data = michelson,
+      main = "Speed of Light Data", xlab = "Experiment No.")
> fm <- aov(Speed ~ Run + Expt, data = michelson)
> summary(fm)
            Df Sum Sq Mean Sq F value  Pr(>F)   
Run         19 113344    5965   1.105 0.36321   
Expt         4  94514   23629   4.378 0.00307 **
Residuals   76 410166    5397                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> fm0 <- update(fm, . ~ . - Run)
> anova(fm0, fm)
Analysis of Variance Table

Model 1: Speed ~ Expt
Model 2: Speed ~ Run + Expt
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     95 523510                           
2     76 410166 19    113344 1.1053 0.3632
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>