X.—CORRELATION : ILLUSTRATIONS AND METHODS. - 207 
follows from the last section, are very nearly linea a resu oth ek ‘ 
confirmed by the diagram of the regression lines (fig. 37, po Bh z 
On the other hand, it is evident from fig. 39, p. 176, that we = 
should expect the two correlation-ratios for Table VI. of the same |. \ * ; 
chapter to differ considerably from each other and from the ¢ x He 
tion. The values found are Ny =0'14, ,=038 (r= -0014)> 
7 18 comparatively low as proportions of male births differ little 
in the successive arrays, but »,, is higher since the line of regres- 
sion of ¥ on X is sharply curved. For Table VIII, p. 183, the 
two ratios are 7,, = 046, 5, =039 (r=0'34). The confirmation 
of these values is left to the student, 
The student should notice that the correlation-ratio only 
affords a satisfactory test when the number of observations is 
sufficiently large for a grouped correlation table to be formed. 
In the case of a short series of observations such as that given in 
Table VII., p. 178, the method is inapplicable. 
CALCULATION oF THE CORRELATION-RATIO : Erample.—Son’s Stature on 
Father's Stature : Data of Table II1., Chap. 1X., p. 160. 
1. 2. 3. 0. 
Type of Mean of LX erie 
Ira Arra " 
Father's | Sond ofall Som Dofeeener Frequency, Frequency x 
Stature). Stature). (68-66). 
59 64°67 -3+00 15-9201 : 47°76 
60 , 6564 - 3-02 91204 35 31-92 
61 | 66-34 - 2-32 53824 8 43-06 
62 65°56 -3°10 96100 17 163-37 
63 66°68 -1-98 39204 335 13133 
66-74 - 192 36864 61-5 226-71 
’ 67°19 — 1-47 2-1609 95-5 206-37 
{ 67°61 ~1+05 11025 142 156-56 
: 67-95 -0-71 0-5041 1375 69-31 
69°07 + 0°41 01681 154 25-89 
« 69°39 +073 0-5329 1415 7541 
69-74 +1-08 1'1664 116 135-30 
i 70°50 +184 33856 78 264-08 
i 70-87 42-21 4-8841 49 239-32 
i 72:00 +3734 11-1556 285 317-93 
‘ 7150 +284 80656 : 32°26 
i- 7173 +307 9+4249 50 51-84 
Total : 1u/8 2218442 
omy’ =2218'42/1078 =2058 omy=143 
Nyz=143/2'75=0"52. 
0.