- THEORY OF STATISTICS. 
frequencies in adjacent compartments, may be of service. The 
correlation table for stature in father and son (Table III, Chap. 
IX.), for instance, is obviously not strictly isotropic as it stands: 
we have seen, however, that it appears to be normal, within the 
limits of fluctuations of sampling, and it should consequently be 
isotropic within such limits. We can apply a rough test by 
regrouping the table in a much coarser form, say with four rows 
and four columns: the table below exhibits such a grouping, the 
limits of rows and of columns having been so fixed as to include 
not less than 200 observations in each array. 
TaBLE I.—(condensed from Table III. of Chapter IX.). 
Father’s Stature (inches). 
Son’s Stature 
(inches). Under , 
! 5_G7T : . 69°5 
655. G5-5-67 SIENG67-5-605.008 ., 7 over, I Total. 
Under 66°5 97°5 74°25 34°75 105 217 
66°5-685 76°5 108 85 52 3215 
685-705 33°25 64°75 95 845 277°5 
70°5 and over 14°75 325 8075 | 134 262 
Total 222 2795 2955 281 1078 
Taking the ratio of the frequency in col. 1to the sum of the 
frequencies in cols. 1 and 2 for each successive row, and so on for 
the other pairs of columns, we find the following series of ratios : 
TABLE IL — Ratio of Frequency in Column m to Frequency in Column m 
+ Frequency in Column (m+1) in Table 1. 
Columns 
Row. 
1 and 2. 2 and 3. 3 and 4. 
0568 0-681 0-768 
0415 0560 0620 
0 339 0405 0529 
0-312 0-287 0376 
These ratios decrease continuously as we pass from the top to the 
bottom of the table, and the distribution, as condensed, is therefore 
330