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Story Name: Speed of Light
Story Topics: Physics 
Datafile Name: michelson.data
Methods: Boxplot , T-test , ANOVA 
Abstract: In 1879, A. A. Michelson made 100 determinations of the velocity of light in air using a modification of a method proposed by the French physicist Foucault. These measurements were grouped into five trials of 20 measurements each. The numbers are in km/sec, and have had 299,000 subtracted from them. The currently accepted "true" velocity of light in vacuum is 299,792.5 km/sec.

The data are given here as reported by Stigler. Stigler has applied the corrections used by Michelson and reports that the "true" value appropriate for comparison to these measurements is 734.5. Each trial may be a summary of several experimental observations.

Because the speed of light is a physical constant, we know (to a close approximation) the "true" value that Michelson was trying to measure. It is therefore possible to test the null hypothesis that the true mean = 734.5 for each of the trials or for all 100 determinations taken together.

 There is evidence of trouble in the data. Boxplots of the trials side-by-side indicate that not all were equally variable nor even centered on the same value. A one-way ANOVA confirms this. One might consider startup effects and underlying bias in the instrument.

Image: Boxplot of the five trials to help see where the differences lie.
Story Names: Speed of Light
Reference: Stigler, Stephen M. (1977). Do Robust Estimators Work with Real
Data: The Annals of Statistics 5:4, 1075.
Authorization: contact author
Description: Michelson's measurements of the velocity of light in air. In
1879, A. A. Michelson made 100 determinations of the velocity of light in
air using a modification of a method proposed by the French physicist
Foucault. The data are given here as reported by Stigler. The numbers are in
km/sec, and have had 299,000 subtracted from them. The currently accepted
"true" velocity of light in vacuum is 299,792.5 km/sec. Stigler has applied
corrections used by Michelson and reports that the "true" value appropriate
for comparison to these measurements is 734.5. Each trial may be a summary
of several experimental observations.
Number of cases: 100
Variable Names:

1. Velocity: Velocity
2. Trial#: Trial number