Experimental methods and mathematical processes—The method of limits—The method of average error—The constant method—Difference thresholds and the probability of a judgment of a certain category.

EXPERIMENTAL METHODS AND MATHEMATICAL PROCESSES

THE experimental determination of absolute and difference thresholds or limina is complicated and difficult. A considerable number of physical and psychological, and, it may be added, mathematical, factors is involved, of varying relative importance in different cases. The result is that different methods of procedure have been found most suitable for different cases. These methods have been traditionally grouped under three (or four) distinct headings, and called the Psychophysical Methods. They are:

1. the Method of Limits (Method of Minimal Changes),

2. the Method of Average Error (Method of Production),

3. the Constant Method (Method of Right and Wrong Cases).

4. A fourth method is generally added to the list, viz.:

5. the Method of Equal Appearing Intervals, or Method of Mean Gradations, but this is really no new method. It owes its special name to the nature of the task which it fulfils, viz. the determination of equalappearing (uebermerklich) sense-distances as distinguished from just perceptible (ebenmerklich) sense-distances. The method which it employs falls under one or other of the first three headings.

There are two things, essentially different from each other, which are commonly confused under this one heading “psychophysical methods,” namely the methods of experimenting in order to obtain data, and the processes of calculation after the data have been collected. To avoid this confusion the words “method” and “process” will be employed throughout this book in the way indicated by their use in the above sentence. It is urged that their general adoption would be advantageous. The cause of the confusion is to be found in the historical development of the subject, for with each of the methods of experimenting a process of calculation was associated and the one name was given to both.

The experimental methods of determining thresholds may be divided into two main groups:

1. Methods in which the stimulus is altered continuously until in the opinion of the subject it fulfils some given condition.

2. Methods in which various values of the stimulus are separately submitted by the experimenter to the subject who expresses a judgment on each of them, classifying them into two or more categories.