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 fourfold table in which the correlation is zero. 

 (Drapers' Company Research Memoirs, Biometric Series, viii. 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 + «) 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 -f-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 oO",- may be read off. 



Illustration (i>. Find the value of „(7,. for the case just given of 

 A'' =1000, |(l+ai) = -619, 4 (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 lefl-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 oO",- is '0514. 



Illustration (ii). Let 



iV=-677l, ^(l-f«i) = -7399. ^ (1 -l- a,) = '9908. 

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

 crossing to right-hand scale we find otr,. = '0635 instead of "0634 actual. 



Abac XXII (p. 34) 



Abac to determine from log %^ and oO"r the value of the equiprobable correlation 

 rp,for a fourfold table. {Drapers' Company Research Memoirs, Biometric Series, 

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



The rule is very simple : Enter the Abac with the proper value of oO-,. 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 7'eached. 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, „£r,.='0514 and (p. xxxvii) log;^==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. 



