EVALUATION OF STOPPING RULES ASCENDING TEST PROCEDURES SIMULATIONS FOR AUDIOLOGICAL USING COMPUTER

Stopping rules for ascending audiological test procedures were evaluated by Monte Carlo simulation. The stopping rules differed in the minimum number of responses required at a level, whether these responses occurred on half or a majority of the ascending series, and whether all or only the most recent ascending series were considered. For all procedures, shallow psychometric function slopes yielded estimated thresholds closer to the level giving 50% detection than did steeper slopes, which yielded estimated thresholds roughly 2.5 dB above the level corresponding to 50% on the psychometric function. Shallow slopes also resulted in decreased reliability across threshold measurements, an increased number of trials required for threshold estimates, and a higher proportion of measurements that had to be repeated. Stopping rules using a two-response criterion were faster than those using a three-response criterion, with only a small decrease in reliability. Among stopping rules using the same number of responses for criterion, differences were seen primarily in efficiency for shallow slopes, particularly for procedures using a three-response rather than a two-response criterion for stopping. Results from these simulations should be useful to standards groups. Hughson and Westlake (1944) recommended that uniform procedures be used for audiological pure-tone threshold tests, and proposed a standard procedure for use with naive listeners. Since then, adaptations of their method have evolved into the various procedures used in audiological settings. Most of them have retained one central feature from Hughson and Westlake--thresholds are estimated by trials at successively higher levels until a subject responds, at which point the stimulus level is decreased and another ascending series is begun. One way in which these procedures differ is the "stopping rule" that determines when the measurement is terminated. In this paper, Monte Carlo simulations are used to compare stopping rules on the basis of accuracy, reliability, and efficiency of the threshold measurement. The Monte Carlo method is "the solution of complex mathematical and statistical problems by random sampling from a simulated population on a computer" (Sokal & Rohlf, 1981, p. 794). Computer simulations allow us to estimate the effects of various procedural manipulations on performance with little investment of experimenter or subject time. Moreover, a subject population can be precisely specified to test hypotheses concerning the relationship of test parameters to subject parameters. As all variables can be controlled in simulations, we can better understand test performance under certain conditions, as well as the relationship of test parameters to certain aspects of human performance. If the results of computer simulations are like results with actual listeners, parameters can be chosen to improve the reliability and speed of testing. Such results should be useful for various standards groups: for example, in selecting stopping rules for automated audiometers. On the other hand, if actual and simulated performance do not agree, then further knowledge of human performance is necessary to improve testing procedures. Thus, our understanding of human performance can be evaluated by comparing actual and simulated (theoretical) performance. Audiological procedures have two phases: a familiarization phase, where a clearly audible signal is presented, and a subsequent threshold-finding test phase. For purposes of the present study, we adopted a standardized familiarization technique and then examined the differences due to stopping rules during the test phase. The stopping rules we examined are those suggested by Hughson and Westlake (1944), Carhart and Jerger (1959), ASHA (1978), ANSI (1978), and ISO (1983), as well as other rules that can be generated using combinations of the features of these rules. The distinguishing features of these stopping rules are