On Correlation and the Methods of Modern Statistics

Abstract

I DO not know that much profit is likely to arise from continuing this discussion further; it appears to me to be merely unwrapping considerable convolutions in Mr. Hinks's mental attitude towards Miss Gibson and myself. The chief charge made at the British Association was that we had overlooked a curved regression line between magnitude and parallax—that now appears to have disappeared into limbo. In his first letter to NATURE Mr. Hinks apparently objected to our finding “a quite significant and important” relation between parallax and proper motion, but one not more than half-way up the correlation scale. He has now discovered that “the point of most general interest” is that of colour. He charged us with stating a far-reaching suggestion on the basis of the Cape stars. It turns out now that the element in our far-reaching suggestion is not the suggestion at all, but what I am prepared to assert as a fact, namely, that the magnitude of the stars “is not mainly determined by parallax or distance, but is more closely associated with colour, and thus probably with chemical or physical condition.” The colour and magnitude correlation is essentially that determined by Miss Gibson, 0.3; the values for the spectral class and magnitude correlations run up according to the classification used to double this value and even to 0.7. The colour and spectral class correlations reach, as we might expect, a still higher value. Meanwhile, the magnitude and parallax relation in its best determination is 0.28. I agree with Mr. Hinks that this is a point of “general interest,” and I am glad that his last letter enables me to assert it, not as “the vaguest of suggestions,” which words had reference to the discontinuity of frequency in star counts, but as a fact which may be slightly modified when more data are reduced, but is substantially correct as I have given it.

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