98 Teachers Appreciation of General Intelligence 
(5) Graphic Exhibition of the Relationship of Clothes and Intelligence. The 
value of the crude correlation between intelligence and clothing found by mean 
square contingency corrected for number of cells was *29. Found by a two-rowed 
Table*, the first row containing Class I of clothing and the second row Classes II — V, 
the correlation ratio was "30, a result very close to the contingency value. It 
appeared worth while investigating the whole problem of the linearity of the 
regression in this case of clothing and intelligence as a justification of the use 
of the correlation methods employed. Accordingly the intelligence categories 
were plotted on a normal scale, the standard deviation of intelligence being taken 
as the unit. At the means of the intelligence groups was set up the means of 
the clothing of such groups, the range of Class II of clothing being taken as the 
unit, and all means measured in terms of this unit from the boundary between 
Classes I and II. In obtaining the mean clothing for any given array of in- 
telligence, we had first to express the mean in terms of the standard deviation 
of the array and then these means in terms of h the range of Class II of clothing. 
The following numerical results were reached, x is measured from upper x from 
lower limit of Class II, a,, and a a . are standard deviations. 
x B l<r a = -6624, x B \<r B = "1744, h\<r B = -8363, <r B /<r a . = 1 '4239, x„jh = -7916, 
Xel<r Q - -7750, x c '/<r c = '4560, h/or b =1-2310, <ri/<r A - "9679, x c /h = -6296, 
x D j(T D = -5899, Xol<r D = -7519, hjv D =1:3418, <r D \<ro.= - 8880, x D jh = -4396, 
x B j<r B = -2776, x B 'la B =l-ll37, h\<r B =1-3913, <r s /& ch = -8564, x E \h = -1995, 
W,f<r, =-'0486, x/I<t f = 1-2021, h/tr, =1-1586, <r p /<r A = 1 -0284, x F jh =--0376, 
x B \v g = - -4152, x e '/cr G = 1 -3739, h/o- 0 = "9587, o-,,/o- ci . = 1 "2428, x 0 /h = - -4835, 
xj<r cl = 3353, x c J<T cl = "8562, h/tr A = 1-1915, — X*/<r c i= '2806. 
For absolute normality the ratio of the S. D. of the array to the S. D. of the 
population should be a constant ; it is clearly rather variable running up at the 
terminal arrays, so that the distribution is not truly homoscedastic. The rj's 
found by the new method f are 
v = -343, rj' = -340, 
The slope of the regression line 
since b and 07 have been taken as our units of clothing and intelligence respec- 
tively. 
Tn this manner the graph has been constructed and it shows, in a remarkable 
manner, how very closely the regression, even with our qualitative scales, is truly 
linear. The general method of plotting characters on normal scales and then 
testing the linearity of the resulting regression deserves fuller recognition ; for 
besides conveying results effectively to the eye, the continual reappearance of 
linear regression when dealing with these qualitative characters is a feature which 
must give greater confidence in the methods applied. 
* Method given in Biometrika, Vol. vn. Formula (iii.), p. 250. 
t Biometrika, Vol. vn. Formula (ii.), p. 249, and illustration, p. 257. 
