Full text: An Introduction to the theory of statistics

IV.—PARTIAL ASSOCIATION. “7 
The following comparisons indicate the association between 
grandparents and parents, parents and children, and grand- 
parents and grandchildren, respectively :— 
Grandparents and Parents. 
Proportion of light-eyed amongst hed _(BO)_2231 _ : t 
children of light-eyed grand parents (Cc) 3178 70:2 percent, 
Proportion of light-eyed amongst the B 8921 
children of not-light-eyed A *» 
7) 
parents . . . 
Parents and Children. 
Proportion of light-eyed amongst the | _ (45) _2524 _ 
children of light-eyed parents «JT (BY 3052 327 percent 
Proportion of light-eyed amongst the _(48) _ 1060 _ 542 
children of not-light-eyed parents. (B) 1956 
In both the above cases we are really dealing with the 
association between parent and offspring, and consequently the 
intensity of association is, as might be expected, approximately 
the same ; in the next case it is naturally lower: — 
Grandparents and Grandchildren. 
Proportion of light-eyed amongst the 0 
grandchildren of light-eyed grand- =U) 2 = 180 per cent. 
parents . : (C) 
Proportion of light-eyed amongst the ) 
grandchildren of not-light-eyed = 11H go 13 kay 
grandparents : : . : () 
We proceed now to test the partial associations between grand- 
parents and grandchildren, as distinct from the total associations 
given above, in order to throw light on the real nature of the 
resemblance. There are two such partial associations to be 
tested : (1) where the parents are light-eyed, (2) where they are 
not-light-eyed. The following are the comparisons :— 
Grandparents and Grandchildren : Parents light-eyed. 
Proportion of light-eyed amongst the B 1928 
grandchildren of light-eyed grand- 420), 1923 864 per cent. 
(BC) ~ 2231 
parents . . 
Proportion of light-eyed amongst the 
grandchildren of not-light-eyed = (42) = or =T28 " 
grandparents . ; > . (87) 
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