Chance-level hit rates in closed-set, forced-choice audiometry and a novel utility for the significance test-based detection of malingering

The primary aim of this study was to extend existing theory on the relationship between chance-level performance and the number of alternatives and trials in closed-set, forced-choice speech audiometry and sound localization methods. When calculating chance performance for closed-set, forced-choice experiments with multiple trials, the binomial distribution should be preferred over the simple 1/a probability, as the latter is appropriate only for single trial experiments. The historical use of constant hit rates for determining chance performance has been based upon the assumption that random hits are distributed evenly across multiple trials. For any closed-set, forced-choice task with 2 to 10 alternatives and 2 to 100 trials, we calculated the probability of obtaining any given hit rate due to random guessing alone according to the binomial distribution. Hit rates with probabilities p > 0.05 were interpreted as being likely to occur due to random chance alone, whereas hit rates with probabilities of p <= 0.05 were interpreted as being unlikely to occur due to chance alone. For sound localization experiments with speakers at fixed positions, the expected probability of a random hit was also calculated using the binomial distribution. The expected angular root mean square (rms) error in sound localization resulting from the random selection of sound sources was investigated using Monte Carlo simulations. A new aspect in the interpretation of test results was identified for situations in which the observed number of hits is much lower than would be expected due to chance alone. For test methods incorporating a relatively low number of alternatives and a sufficiently high, yet clinically feasible, number of trials, both upper and lower thresholds for chance-level performance could be identified. This lower threshold represents the lowest hit rate which can be expected through random chance alone. Extending interpretation of results to include this lower threshold affords the ability to not only identify performance significantly superior to that of chance, but also that significantly poorer than chance and thereby represents a simple method for the objective detection of malingering.