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The comparison of series of measures

Published online by Cambridge University Press:  24 October 2008

Harold Jeffreys
Harold Jeffreys
Affiliation:
St John's College
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Extract

We often wish to test the difference of the means of two series of measures of a quantity for a systematic difference. A suitable test, in terms of the theory of probability, can be obtained as follows. We suppose that in each series the probability of error is normally distributed with unknown standard error. Then if we have only one observation in each series, the difference of the two could equally well be interpreted as entirely due to the random error in one series, the other being right, or entirely due to systematic difference, both observations being free from random error. This suggests that we should take as one of our fundamental quantities the expectation of the difference of a single measure in one series from one in the other; the expectation of the square of the difference, however, appears still better.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 1 , March 1937 , pp. 35 - 40
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

* Cf. Phil. Mag. 22 (1936), 354.Google Scholar

* The information given by the examination would be more accurately conveyed by publishing a list in order of merit with a standard error of the position corresponding to the sampling error, which is determinable.

† Mon. Not. R. Astr. Soc., Geophys. Suppl., 3 (1936), 423–43.Google Scholar

* The observations indicate a departure from the normal law of error, which is allowed for by a suitable system of weighting. The equivalent number of observations is the weight of the determination when unit weight corresponds to the standard error found for a normal observation. This complication does not affect the use of the results for illustration.

† Proc. Camb. Phil. Soc. 32 (1936), 430.Google Scholar