Egon S. Pearson 
33 
to divide the observations of each series into " groups," and thus we have the 
50 observations 
^1 ; ^2, ••• Vm form Group 1 with mean and standard deviation a^, 
y^.y-i, ■■■ 2/51 „ „ 2 „ „ d, „ „ „ 0-2, 
yk , yk+i, ■■■ Vm+k-i „ >, „ „ dk „ „ „ o-fc, 
Vu, 2/15. ••• y&i n „ 14 „ „ du „ „ „ 0-14. 
By "the correlation of successive judgments at intervals of one," I shall under- 
stand the correlation of the 50 observations of Group 1 of a series with the 50 
corresponding observations of Group) 2 of that series ; this will be expressed 
as pi. Similarly "the correlation of successive judgments at intervals of k" or pk, 
is the correlation of the corresponding observations in Groups 1 and k + 1. In feet 
Pk IS given by 
\ 50 
5 Q - IhUf+k - dAk+i 
Pk = — ^iv). 
0-1-0-^+1 
When these constants are to be referred to souk,' particular series, say the 
^th, the prefix p will be placed before them, e.g. , ^aj^, j,pk, etc. 
A comparison of the d's, cr's and p's of the different series will be instructive, 
but as each of these constants has been calculated from 50 observations only, to 
obtain quantities with smaller probable errors we must combine the observations 
of the 20 series. Thus we shall obtain 
= i- 2 k = ^ S {du) (v), 
mu „, ill ,„ 
where = 50, the number in a group, 
m — 20, the number of series, 
and % indicates summation for all 20 series. 
= — S (pkCTiak+i + dA+i) - D,Dk+i. 
Pk=^ ^ (pkcr, (Tk+,) + -t (A - d,) (A+i - dk+,) in view of (v) . . .(vi). 
Putting k = 0, in (vi) we have as the square of the standard deviation 
and similarly 
m «, m 
S\^, = ^t{a\^,)+~tiD,^,-dk,,) 
fit jn f'f' ni 
.(vii), 
Biometrika xiv 
