This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1899 Excerpt: ...Nr'o-o-' = S nini (M-m) (M'-m') = S (n,n,MM')-Nwm', since m = S (n,n,M)/N, m' = S (nM'J/N. Thus: S (nMMQ/N-mm' (xxvii.). If o-„ and a-'a be the standard deviations of the means of the arrays of uncles and nephews and R the correlation of these means, the numerator is clearly Ro-,,0-',,. Thus: r = K-=-=7.. (xxvin.). aa x' Here the numerator as a whole or in parts is easily found from the means of the VOL. CXCXI.--A. 2 N arrays. If cr0 and r'0 be the means of unloaded uncles and nephews, we note that they are arrays owing to common parentage, and hence their array standard deviations will be cr0 y/l--pz and cr'0 /l--p2, p being the standard deviation of parent and offspring. As before we find: a = ai + a% (1-p') (xxviii.). =+(l-p2) J If, as will probably be the case, there be no secular change between uncles and nephews, then cr = cr', r„ = cr'a, cr0 = cr'0, and accordingly r = Rcr;;/cr2; whence, using (xxiv.), we have: r = r X R X-j =j (xxix.). If we could assume cra = cr„ and r = cr, this result would reduce to the very simple form: r' = r X R. Now the assumption cr„ = cr0 is, I think, legitimate, for the distribution for an unloaded array of nephews or uncles should be sensibly that of an array of brethren. But the equality of cru and o-0, which would now involve that of a and cr, is a much more doubtful point. cr„ and ra mark indeed quite different systems of loading. Both, it is true, are of the form S (nn'W) IN-S (nn'M) / N 2, but in the case of brethren n = (n--1) or n has perfect correlation with n, while in the case of uncles and nephews n is only imperfectly correlated with n. The intensity of this correlation depends upon the correlation between the sizes of arrays of uncles and nephews, a quantity which may be very sm...
"synopsis" may belong to another edition of this title.
(No Available Copies)
If you know the book but cannot find it on AbeBooks, we can automatically search for it on your behalf as new inventory is added. If it is added to AbeBooks by one of our member booksellers, we will notify you!Create a Want