Egon S. Pearson 
27 
and perhaps too from a relationship between the successive YfS. There may be no 
large scale sessional change, and it may be possible to correct for a secular change 
in personal equation, but even then the mean of a small number " 771 " of successive 
observations, subject to its probable error •6745 /y/^ will not be a satisfactory 
approximation to the true value of the quantity observed, if these "iu" observations 
are correlated. Suppose for example that the points in Figure 14 (p. 76) represent a 
series of successive observations which have been corrected for any secular change 
in personal equation ; the linear sessional change is small and has been represented 
by the continuous straight line, while the dotted straight line represents the mean 
value of the 68 observations. Yet many sets of 10 consecutive observations could 
be taken, the difference between the mean of which and that of the whole 63 
would be far greater than would be anticipated from the value of the probable error 
calculated from the expression above. This is because the observations are not 
randomly distributed in time. 
In addition to secular and sessional changes in the value of an estimation, there 
may be similar changes in the standard deviation; the judgments may become 
more erratic or less so. A sessional change giving an increase in standard deviation 
would suggest the effect of fatigue ; and secular change decreasing the standard 
deviation might be the indication of increased accuracy with experience. An 
example of secular change in personal equation and standard deviation is illustrated 
in the diagram on p. 84; the details of this will be discussed more fully in the 
reduction of Experiment D, but it is here sufficient to say that the central curve 
represents the smoothed personal equation, while the distance between any point 
on this curve and either of the outer curves gives the smoothed standard deviation 
at that point or period in the series of observations. It will be seen that the 
standard deviation inci-eases in the later observations. 
It would be out of p'lace at this point to enter further into the details of 
variation in personal e<iuation and correlation of judgments, but I think that 
enough has been said to indicate the general lines of enquiry. In choosing the 
experiments which will be described in the following sections, the aim has been 
to select those in which there was likely to be considerable variation in judgment, 
and where consequently the secular and sessional changes, if present, woidd be 
clearly recognizable and the correlation of successive judgments easy to measure_ 
It was also important that the errors in measurement should be small compared 
with the variations in judgment. 
It may of course be urged that the experiments should have been carried out 
by an observer who was unaware of the lines of enquiry and therefore not liable to 
bias of any form, but this was not practicable, and in fact none of the reductions 
had been completed nor the general theory developed before all the experiments 
had been carried out, and I do not think that the observations could have been 
affected by any conscious or unconscious prejudice. 
