Xv1L.—NORMAL CORRELATION. 25 
and inserting o,=272, 0y= 275, r,;=051, sin f=cos §=1//2 
find oz=3'361). Drawing a diagram and fitting a normal 
curve we have fig. 51 ; the distribution is rather irregular but the 
fit is fair ; certainly there is no marked asymmetry, and, so far as 
the graphical test goes, the distribution may be regarded as 
appreciably normal. One of the greatest divergences of the 
actual distribution from the normal curve occurs in the almost 
central interval with frequency 78: the difference between the 
observed and calculated frequencies is here 12 units, but the 
standard error is 9'1, so that it may well have occurred as a 
fluctuation of simple sampling. 
LA : — . 
8¢ 
k 
Fie. 51.—Distribution of Frequency obtained by addition of Table III., 
Chap. IX., along Diagonals running up from left to right, fitted with a 
Normal Curve. 
11. So far, we have seen (1) that the regression is approxi- 
mately linear; (2) that, in the arrays which we have tested, the 
standard-deviations are approximately constant, or at least that 
their differences are only small, irregular and fluctuating ; (3) that 
the distribution of totals for one set of diagonal arrays is approxi- 
mately normal. These results suggest, though they cannot 
completely prove, that the whole distribution of frequency may 
be regarded as approximately normal, within the limits of fluctu- 
ations of sampling. We may therefore apply a more searching 
test, viz. the form of the contour lines and the closeness of their 
fit to the contour-ellipses of the normal surface. We can see at 
once, however, that no very close fit can be expected. Since the 
frequencies in the compartments of the table are small, the 
standard error of any frequency is given approximately by its 
acy