OF ERROES OF JUDGMENT AND ON THE PERSONAL EQUATION. 
285 
Relative Equation (3-2), A glance at the diagram shows the great iri’egularity oi 
the distribution in this case. The outlying group on the left is liere quite easily 
accounted for by the skew curve. It is immensely improbable on the basis of a 
normal distribution. The outlying group of three observations on the right contriljutes 
17 to the of the skew curve and only 2‘7 to that of the normal curve. The peak 
costs the normal curve 29 and the skew curve 16. If we were to cut oft the two 
extreme groups the y' for the skew curve would be reduced to about 40, and for 
the normal curve, to about 75. Thus the skew curve, without re-calculation ot 
constants, would still be immensely more probable than the normal curve. There 
is little doubt, however, that there is some source of change in the personal 
equation of Dr. Lee which has produced the anomalies in the relative judgment 
of Dr. Macdonell and herself 
Relative Equation (2-1). The small probability of the skew curve and the 
“ practical impossibility ” of the normal curve depend entirely on the existence 
of the outlying observation to the right. The y~’s in both cases would be 
reduced to about 24, and thus give probable results on the basis of random 
samplings if tliis outlying observation were removed. A re-calcidation of constants 
would set the skew curve far alcove the normal, for its constants are more widely 
modified l)y outlying observations. 
As I have already pointed out the value of y' depends largely on wbiere the range 
for the grouping of the frequencies is taken, and the tails largely determine what 
its value will be. But I have endeavoured to be equally fair to both theoiies, and 
rough as the numbers must necessarily be, we may still safely conclude that the skew 
curve gives infinitely more probable results than the normal. Indeed, with the 
rejection of an outlying observation or two, we could bring the whole skew-series 
into the range of probalde random samplings, but we should fail to achieve this in 
the case of the normal curve without much “ doctoring,” which would have to be 
applied in certain cases to the very body of the observatioirs and not only to its tails. 
Personally while considering that the value of y~ is a very good criterion for the 
rejection or not of outlying observations, as soon as a ■prohahle laiv for the 
distribution of errors has been determined, I have thought it right not to reject one 
single observation"^'" after the constants had once been determined, because I had in 
view the comparison of two different theories, and sucli rejection might apparently 
favour one or the other tlieory. 
I now turn to the results fin- the bisection of lines ; the probabilities fin- the 
random sampling in these series are given in Table XX. 
* In the bright-line experimente 520 were oiiginally made, as I supposed when we came to examine the 
r-ecording strips some obvious slips or blunders would be I'ound, and I left myself a margin of 20 for such. 
Only one experiment, however. No. 291, seemed to be a failure, the recording mark of one observer being- 
in this case quite removed from the part of the scale occupied by the bright line. 
