xlii Tables for Statisticians and Biometricians [XXI, XXII 



Abac XXI (p. 33) 



For determination of the standard-deviation of the correlation coefficients obtained 

 by random sampling from a four-fold table in which the correlation is zero. 

 (Drapers' Company Research Memoirs, Biometiic Series, vm. G. H. Soper's Abac.) 



Method of use : Enter with the total frequency of the sample on the left-hand 

 scale, and with the first value of \ (1 + o) on the bottom scale. The horizontal 

 through the former and the vertical through the latter meet at a point. At this 

 point pass up the diagonal to the left-hand scale again. Where you meet that 

 scale pass along the horizontal until you meet the vertical through the second 

 value of | (1 + a). Then from this point pass along the diagonal again to the left- 

 hand scale, whence traverse the horizontal to the right-hand scale and there the 

 required value of cr r may be read off. 



Illustration (i). Find the value of cr r for the case just given of 

 JV=1000, ^(1+« 1 ) = -619, |(1 + a„) = -622. 

 The vertical through '619 meets the 1000 horizontal in a point whose diagonal 

 reaches the left-hand scale almost exactly in 620. Whence passing horizontally 

 we reach the vertical through - 622 in a point about midway between two diagonal 

 lines. Passing up midway between these two diagonals, we reach almost exactly 

 the 380 line on the left-hand scale. Passing across to the right-hand scale along 

 this line, we see that we are slightly above the middle of the division between 

 •050 and '052, say '0512. The actual value of a r is "0514. 



Illustration (ii). Let 



JV=-6771, |(1 + «0 = -7399, |(1 + a 2 ) = '9908. 

 A similar process gives first 450 ou left-hand scale and then about 248, whence 

 crossing to right-hand scale we find cr r = - 0635 instead of "0634 actual. 



Abac XXII (p. 34) 



Abac to determine from log %' 2 and a r the value of the equiprobable correlation 

 r P ,for a fourfold table. (Drapers' Company Research Memoirs, Biometric Series, 

 vm. G. H. Soper's Abac.) 



The rule is very simple : Enter the Abac with the proper value of a r on the 

 scale at the foot and rise on the vertical till the horizontal through the proper 

 value of log^ 2 on the left-hand scale is reached. Then follow the curve through 

 the meet of these two lines to the right-hand scale, where the requisite correlation 

 will be found inscribed. 



Illustration. Take the Table for Eye Colour in Father and Son given on 

 p. xxxiv. Here, as just shewn, ov="0514 and (p. xxxvii) log^ 2 =2'1249. If we enter 

 with the vertical through - 0514 on the scale at the bottom, and the horizontal 

 through 2 - 1249 on the left-hand scale, the curve through their point of intersection 

 reaches the right-hand scale just below the "53 mark, say "529. This agrees with 

 the correlation found above (p. xxxviii) by interpolation from Table XX. 



