The essentials of mental measurement / by William Brown.

  • Brown, William, 1811-
Date:
1911
Catalogue details

Licence: In copyright

Credit: The essentials of mental measurement / by William Brown. Source: Wellcome Collection.

Provider: This material has been provided by King’s College London. The original may be consulted at King’s College London.

    74/172 (page 62)
    Quite recently, however, an empirical investigation has been made on samples of 4, 8, and 30 cases, taken from a total population of 3000 pairs of measurements (height and left middle finger measurements of 8000 criminals; real correlation, •66)*. In the case of correlation it was found that when the original pairs of measurements were arranged so that the real correlation was 0, the distribution of the values of r obtained from samples of n was given approximately by the formula n-i 2/ = 2/o(l -x') ^ • Five distributions in all were worked out, giving the follow- ing moment coefficients: Samples of 4 {r = 0) 8 (r = 0) 4(r = -66) 8(r=-66) „ 30(r = -66) Mean •5609 •6139 •661 S.D. •5512 •3731 •4680 ■2684 •1001 •3038 •1392 •2190 •07202 •01003 Ms •1570 •02634 •000882 M4 •1768 •0454 •2152 ■02714 •000461 ^1 2-245 1-857 -7713 P-2 1-918 2.336 4- 489 5- 2.32 4-580 [Unit of grouping for 4's and 8's = ^04.] Correlation results, for real value of r = -66, were samples of 4 -561 ± Oil, „ 8 -614 + -065, „ 30 -6609 ± •0067. Hence it may be concluded that, although in the case of such small samples as 4 or 8 the ordinary formula for the p.e. of r gives much too low a value, yet in the case of as many as 30, the formula applies with tolerable accuracy. We must, however, bear in mind that this result has only been proved (empirically) to hold in the single case where the actual correlation was '66. ♦ Student : The Probable Error of a Coefficient of Correlation, Bio- metriha, Vol. vi. PP- 302-310. 1908-1909.