Survey of the Colour Vision of 1000 Students, 193 



material ? It is possible to answer tins question by com- 

 paring the observed distribution with one calculated by the 

 formula and determining a function P from a table given 

 in the Tables above referred to. If for example P comes 

 out *20, in 20 out of 100 trials we should get in random 

 sampling a fit as bad or worse than the observations actually 

 give. It is not possible to specify exactly when a good fit 

 ends and a bad one begins, but apparently above *3 is good 

 and above "1 not unreasonable. The final value of P depends 

 considerably on how the distribution is grouped. 



When P is worked out for the observations recorded in 

 the former paper, assuming a Gaussian distribution, the 

 value for the 43 men is "73 and for the 38 women '14, but 

 by taking the women in five groups the value for P becomes 

 as high as *6. Consequently the Gaussian distribution is a 

 good fit, and no significance is to be attributed to the 

 minimum at 14 referred to on p. 584 of the former paper : 

 it was due simply to the number of observers being so small, 

 and would have vanished, had there been more of them. 



The results of the red-green test for the men are shown 

 by fig. 5. One of the observers could not distinguish the 

 red disks from the green disks even when" perfectly focussod, 

 another could just distinguish them when focussed, and a 

 third distinguished them one millimetre out of focus on the 

 other side. These three are grouped together in the rect- 

 angle from to 1. Some doubt might be expressed as to 

 whether this is justifiable, but it does not affect the estimate 

 of goodness of fit appreciably, as for this purpose the first 

 ten observers were grouped together. The broken line 

 represents the graduation of the data by the formula 



P — v tan - xja 



where ?/ = 30'82, p = 5*695, m = 5799, a = 7'94C, and the 

 origin is taken at 19'942. This is the most suitable formula 

 according to the classification, since fti = m 6203 and /3 2 = 4*981. 

 It gave P = *008. An attempt was also made to represent 

 the data by the formula y x~ p e~ y , but it gave a value of P 

 less than one ten-millionth. It is not so much the presence 

 of the tail on the left as the fact that the central maximum 

 is too symmetrical, that makes it difficult to represent the 

 whole distribution by these formula 1 . 



We next tried to represent the results as the superposition 

 of two Gaussian distributions, a. large one with its mean at 



Phil. Mag. S. 6. Vol. 41. No. 242. Feb. 1921. 



