Bauhaus-Universität Weimar

The New Psychology
Scripture, Edward Wheeler
made on six persons the constant colour appeared of 
longer duration than the changing one in 58.7 % of the 
cases. The conclusion is drawn that the constant 
colour actually seemed of longer duration. 
What degree of validity is to be given to this state¬ 
ment ? When it is required to say that one of two 
things is longer than the other, mere guess-work with¬ 
out any knowledge would make one of them longer in 
50% of the cases. Here we have 58.7% for one of the 
things. Making the supposition that absolutely no 
errors were made in setting up the problem and carry¬ 
ing out the experiments, we find that according to the 
theorem of Bernoulli P=o.24, or that the degree of 
validity is about £ on the scale of certainty which we 
have assumed. Of course, for a less stringent scale the 
degree would be greater. 
Up to this point we have treated of mathematical 
probabilities ; we have assumed an ideally perfect die, 
or we have supposed the statistics to be absolutely 
free from error. To such cases we can apply the 
laws of chance as given in mathematical works on 
probability. In actual investigations, however, it must 
first be proven that the results follow the laws of 
Suppose we have as the result of a statistical investi- 
gation the fraction —where ri is the total number of 
cases and in' the number that have a certain character ; 
can we assume that the co-efficient of frequency p,=s^ 
can be treated as a mathematical probability pi For 
example, in the case of time-estimate just considered n' Jj: 
600, w' = 352 and p' = 0.587; we have treated p' as a 
mathematical probability, and we must ask if this treat¬ 
ment was justifiable. 
If p' is a mathematical probability, a repetition of


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