xlii 7'nl>li* /;// Statistician* <i/t</ /ii'mnfricinns [XXI. \.\II 



ABAC XXI (p. 33) 



For determination of the standard-deviation of the correlation coefficients obt< 

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

 (Drapers' Company Research Memoirs, Biometric Series, vill. 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 (l + a) 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 4 (1 +o). Then from this point pass along the diagonal again to the loft- 

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

 required value of <r r may be read off. 



Illustration (i). Find the value of O o> for the case just given of 



#=1000, 4(1+ a,) = -619, i (! + *) -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 O o> is "0514. 



Illustration (ii). Let 



#=6771, $ (! + ,) = '7399, (1 + 2 ) = -9908. 



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

 crossing to right-hand scale we find O o> = '0635 instead of '0634 actual. 



ABAC XXII (p. 34) 



Abac to determine from log ^ a and O f r the value of the equiprobable correlation 

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

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



The rule is very simple : Enter the Abac with the proper value of O o> on the 

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

 value of log ^* 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, O o>='0514 and (p. xxxvii) logx'=2'1249. If we enter 

 with the vertical through '0514 ou 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. 



