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STA TISTICS: PEARL A ND LEBLA NC Proc. N. A. S. 
lated on the basis of this coarse grouping. Call these values (^2. Then 
what we wish to know is the value of the correlation r^^^.^. 
This was calculated by the direct product moment method, without 
grouping and gave as a result 
r^^4>2 = + .84 ± .02. 
It is at once evident that we are dealing here with a high degree of 
correlation. That the regression is linear is indicated by the spot dia- 
gram of the correlation surface shown in figure 1. 
This result indicates that whenever it is impossible, by reason of un- 
satisfactory tabulation of the original raw statistics, to get any but a 
coarse age grouping, we may still use the age index (f) with confidence that 
it will reflect closely the differences in population in respect of age distri- 
bution. The test here given is obviously a severe one, because all adult 
ages are thrown into one group. But even so, the correlation is high. 
With such a value of r as this, it is obvious that one could, by means of the 
appropriate regression equation, determine corrections for the 02 values, 
giving predicted or calculated </)i's which would with extreme accuracy 
approximate the true values. 
The means and standard deviations are as follows : 
Mean ct>i = 27.27 =t= 1.46 
Standard deviation 01 = 21.53 ± 1.03 
Mean 02 = 19.71 ± 1.23 
Standard deviation 02 = 18.14 ± .87 
As would be expected the 02 mean is lower than the 0i mean, and 02 is 
less variable, as indicated by the standard deviation, than 0i. The 
difference in the means is large, but this is of no great importance in the 
practical use of the age index. It is of much greater practical significance 
that the difference in the variabilities is not large. If we could trust here 
the theory of simple sampling (which we probably cannot) the difference 
between the standard deviations could not be regarded as certainly signifi- 
cant at all. The more important consideration is that 02 is reflecting in 
its standard deviation 84.2 per cent of the variation among these 99 Iowa 
counties in respect of age distribution of their populations, as measured 
by 01. 
In conclusion it may be stated that since, as is demonstrated in this 
paper, there is a high correlation between the values of 0 for extremely 
coarse age groupings, with the values obtained from finer groupings, this 
age index may be used with considerable confidence in cases where data on 
age distribution are available only for a few broad classes covering the life 
span. All our experience with this age index 0 since its publication two years 
ago has confirmed our belief that it is a function of great value to the vital 
