Obvious skewness of many psychophysical curves—Pearson's test for goodness of fit applied to the method of average error—Applied to the method of right and wrong cases—Skew curves in homogeneous material—The summation method of finding moments—Calculation of a skew curve—Analysis into two normal curves— Conclusions.

OBVIOUS SKEWNESS OF MANY PSYCHOPHYSICAL CURVES

To anyone accustomed to handling distribution data, a most striking point about the results of many psychophysical experiments is the obvious skewness of much of the data. Both the examples used extensively in the previous chapter show this very strongly as can be seen from an inspection of the data either in numerical or diagrammatic form, and also from the various values of the threshold T found by the different processes of calculation: for these differences arise largely from the fact that the distribution is not normal.

Taking the best of the processes, the Constant Process, it is of interest to see how closely the curve which it gives fits the original data. A method of thus estimating the goodness of fit of curves has been given by Professor Karl Pearson. His method is perfectly general, and applicable to all classes of curves, but it has been most fully worked out for the fitting of bell-curves to histograms. Our problem is not of this nature, though it might appear to be so, for the pseudo-histogram (Fig. 8) which can be formed from the frequencies p differs essentially from a real histogram. Since in psychophysics it may often be necessary to fit curves to real histograms, for example those obtained in the Method of Average Error, we shall first explain Pearson's Goodness of Fit Test for this case, using the bisection data of Chapter II for the purpose (see pp. 15 and 42 and Fig. 6).

PEARSON'S TEST FOR GOODNESS OF FIT APPLIED TO THE METHOD OF AVERAGE ERROR

The bisection data had a mean of 60-13 mms. and a standard deviation of 1-38 mms. With these values, using Sheppard's Tables, we draw the smooth curve shown in Fig. 6. Now it is important at the outset to realise that whether that curve is a good or bad fit to the data depends on the number of observations made. The number in this case was only 29, and it will presently be shown that the curve is a very good fit.