# Bauhaus-Universität Weimar

### Volltext The New Psychology

Titel:
The New Psychology
Person:
Scripture, Edward Wheeler
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit16063/41/
```STATISTICS.
23
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
probability.
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 ;
f7l'
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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