Efficient adaptive procedures for threshold and concurrent slope estimates for psychophysics and speech intelligibility tests

The minimum standard deviations achievable for concurrent estimates of thresholds and psychometric function slopes as well as the optimal target values for adaptive procedures are calculated as functions of stimulus level and track length on the basis of the binomial theory. The optimum pair of targets for a concurrent estimate is found at the correct response probabilities p1 = 0.19 and p2 = 0.81 for the logistic psychometric function. An adaptive procedure that converges at these optimal targets is introduced and tested with Monte Carlo simulations. The efficiency increases rapidly when each subject's response consists of more than one statistically independent Bernoulli trial. Sentence intelligibility tests provide more than one Bernoulli trial per sentence when each word is scored separately. The number of within-sentence trials can be quantified by the j factor Boothroyd and Nittrouer, J. Acoust. Soc. Am. 84, 101-114 (1988). The adaptive procedure was evaluated with 10 normal-hearing and 11 hearing-impaired listeners using two German sentence tests that differ in j factors. The expected advantage of the sentence test with the higher j factor was not observed, possibly due to training effects. Hence, the number of sentences required for a reliable speech reception threshold (approximately 1 dB standard deviation) concurrently with a slope estimate (approximately 20%-30% relative standard deviation) is at least N = 30 if word scoring for short, meaningful sentences (j approximately 2) is performed.