V 1 1 1 IX] lnlr<nlin'ti<ni 



If we iv-niT.-ui^e these Ubles in st:iinlanl form, W9 h;i\- : 



and we see at once that ac? be is negative for all of them, or the rf/^T 

 found from the part of the tables for negative correlation: i.e. r = "5189 

 next place in every case the n u , n u ', n v , n v ' of the quadrant to be found is 

 the standard form. Hence we have, by equation (v), 



is to be 



In the 



the d of 



where the d/N'a are to be found from our present table. To use these, however, we 

 require to ascertain the h and k corresponding to the above four tables. This is 

 most easily done by the use of the first and last columns in Table XXIX of the 

 Tables for Statisticians, Part I, which give h (or k) for (1 a) to five figures, or 

 we can obtain more figures from Table II of this Part n. In the present case we 

 have: 



or: &! = -35045, &j = '75541, 



f\ f n * 7 1 V / ^ ** - * 7 n 



UI . ft2 * I** i t/, /t2 * t/dTB-L, 



-a fca ) = '354, or: A 8 = '35045, & 8 = '37454, 

 -a &1 ) = '354, or: A 4 = '71275, & 4 = '37454. 



For most cases h and k to five decimal figures are fully adequate. 



If the four tables be now worked out by the interpolation formulae using first 

 four entries, and secondly twelve entries (i.e. formulae (a) and (ft) of p. xviii above), 

 we find : 



(ft) 27-113 12-752 56437 28'348 



(a) 27-313 12-847 56'674 28467 



Observed values : 19 10 43 22 



In both cases linear interpolation alone has been used to deduce the value 

 of d for r = "5189 from those found for r=-'50 and ? = '55. These latter 

 values of d have been obtained from the corresponding h's and k's by (a) and (ft). 

 It will be seen at once that (a) and (ft) are in very close agreement, and that, at 

 any rate in this portion of the tables, the hyperbolic formula (a) is fully adequate 

 for most practical statistical purposes. 



!(!-*,) = >363 > 

 (1 - a hl ) = -238, 



