XVIII XX ] 



/Hti'ttf/itrfiiw 



ci\ 



Illustration. The following markedly anomalous series of observations were 

 made by Dr R. A. Houston on the Colour- Vision of Male Student*, the Rayl-igh 

 test being used*. 



In the first column is given the central value of the Logarithm of Ratio Red to 

 Green, in the second the Frequency. 



The mean = - 0'20305 and the standard deviation = -24357. 



(a) We ask first what frequency to expect below 1'30. 



(1-30 - -20305)/-24357 = 4-50, 



and |(1+ a) ='9999966, or $(1 -a) = '0000034 



is the chance of a single individual occurring below 1*30. Thus we should expect 

 only '001,438 individuals in 423 trials, or the negative tail beyond T30 is 

 wholly anomalous. 



We now turn to the three individuals at the positive end of the scale, and 

 ask how many individuals it is reasonable to expect beyond say + "55. Having 

 removed five cases from the negative end of the range we now recalculate mean 

 and standard deviation of the remaining 418 individuals, and find: 

 Mean = - '18299 and standard deviation = '14999. 

 From these values we have : 



(-55 + '18299)/'14999 = 4-887, whence J(l + a) = '999,9995 ; 



or, the chance of one person beyond + '55 is -000,0005 ; we should therefore expect 

 '0002 individuals, not three, in 418 trials. We must therefore exclude the cases 

 at '62, '87 and 1'07. 



(/9) Here we have 



* = 845/846 = '99882, 



or i(l+t)= '99941, 



ka- = 3-245 x '24357 = '79038. 

 * Proc. R. S. Vol. 102, A, p. 353, 1923. f I.e. 2-905 to 2-955. 



