Egon S. Pearson 
71 
(b) The Combination of the Series. 
For the combined series, the coefficients of correlation of successive judgments 
Rjfc for k = \, 2 ... 13 were calculated from 13 correlation tables each based on 
the 1000 combined observations; the results for Dk, Sk and are tabled below 
(Table XI). The effect of the slight sessional change is noticeable in the increasing 
values of D^. 
Using the values of D^, and Rfc and of j,/4 from Table X, Equations (vi), 
(vii) and (viii) give S (pio-io-fc+i) and S (o-^.") for ^; = 1, 2... 14. Equations (ix) 
m m 
and (x) then give the values of *SV and R^' contained in the 5th and Gth rows of 
Table XI. The value of R/ found by this method should be compared witJi that 
found with the help of the p/s, Ci's and o-o's of the individual series, namely 
S(/)iO-iO-2) 
R/ = — ;" = + -3578 + -0186 (x) bis. 
V III III 
The difference which is well within the probable error arises from the fact that 
Ri has been found by grouping the observations in a correlation table, while the 
Pi's, o-j's and cto's were found by direct multiplication of the crude values of the 
observations. 
Another method of obtaining the R/'s is from the first difference correlation 
equations, or the method of Problem 1, p. 41 ; the results are given in the 
7th row of Table XI, while the constants ^Rk, the coefficients of correlation of 
successive first differences required in the solution, are in the 8th row of the 
Table. Comparing the values of "R^ found by the two methods, we find good 
agreement up to k = 6, but beyond this point the R^'s of the second and approxi- 
mative method assume much too large negative values*. It is however evident 
from the results of the first method that Rj' does become negative, and as it 
could not remain negative indefinitely as k increased, there seems here to be 
another indication that a periodic variation exists among the judgments at any 
rate in a certain number of the series. For a complete period covering from 
20 to 22 observations suggested by the yt diagram, R/ should have a minimum 
value at Rj„' or Rj/ ; the figures suggest that the minimum occurs somewhat 
earlier, at about Rg', but the probable errors for these small coefficients are very 
large. When time is available it would be interesting to examine further the 
significance of this periodicity. 
The points (R^;, k) and (R^', k) have been plotted in Figure 12. 
It will be noticed that the Sk's. in the later groups are larger than in the 
earlier, this suggesting again as in the case of the Trisections, that the obser- 
vations become slightly more erratic towards the end of a series. 
* This result tends to confirm the suggestion made on p. 60 that the difference correlation method 
gave too large negative values for R^." in the Trisection Experiment. 
