The Staircase-Method in Psychophysics

Abstract

NOTES AND DISCUSSIONS THE STAIRCASE-METHOD IN PSYCHOPHYSICS A psychophysical method variously referred to as the method of up and downs, 1 the Bekesy audiometric method, 2 or the staircase-method, has come into extensive use in the last few years. The method has several advantages over other more commonly used techniques but it also has some disadvantages. This paper will illustrate the use of the method, will discuss its relative merits and demerits, and will describe a modification which overcomes certain of the disadvantages of the method. The staircase-method is best described by illustrating its use with a specific prob- lem. Suppose the problem is to determine S's absolute, intensive threshold for the sound of a click. The first stimulus that E delivers is a click of some arbitrary intensity. S responds either that he did or did not hear it. If S says 'yes' (he did hear it), the next stimulus is made less intense, and if S says 'no,' the second stimulus is made more intense. If S responds 'yes' to the second stimulus, the third is made less intense, and if he says 'no,' it is made more intense. This procedure is simply continued until some predetermined criterion or 'number of trials' is reached. The results of a series of 30 trials are shown in Fig. 1. The results may be recorded directly on graph-paper; doing so helps E keep the procedure straight. There are a number of ways of determining the intensive value that represents the threshold. The simplest is to compute the mean of the values of a given num- ber of stimuli delivered after the series has reached its final level. This requires an arbitrary decision about when the final level has been reached. The technique, which avoids this difficulty and yields a 50% value, is simply to determine the stimulus above which 50% of the responses are 'yes,'-i.e. in Fig. 1 between 61 and 62 db. Statistical treatment of the results has been discussed by Dixon and Massey, who describe the techniques for determining the means, standard deviations, standard errors, etc., for this type of data.3 The treatments assume, however, that the response to each stimulus is independent of the preceding stimuli and pre- ceding responses. This assumption holds for the examples analyzed, but there is evidence that the assumption does not always hold for human Ss in psychophysical experiments.• The development of techn.iques that take the existing inter-actions into account has not as yet been achieved. W. J. Dixon and F. J. Massey, lnt,.oduction lo Statistical Analysis, 1957, 279· •Georg von Bekesy, A new audiometer, A'la 010-/a,.yngol., 35, 1947, 411-422. •Dixon and Massey, op. cit., 286. • W. S. Verplanck, G. H. Collier, and J. W. Cotton, Nonindependence of succes- sive responses in measurement of the visual threshold, /. exp. Psycho/., 42, 1952, 273-282; Verplanck and Cotton, The dependence of frequencies of seeing on pro- cedural variables: J. Direction and length of series of intensity-ordered stimuli, /. gen. Psycho/., 53, 1955, 37-47; V. L. Senders, Further analysis of response se- quences in the setting of a psychophysical experiment, this JOURNAL, 66, 1 953, 215-229; R. S. Woodworth and Harold Schlosberg, Experimental Psychology, 1954,