Contributions of internal noise and Bernoulli variance to the variability in multiple estimates of d′.
Walt Jesteadt · The Journal of the Acoustical Society of America · 2004
Multiple estimates of d′ obtained from the same observer will vary as a result of differences in attention and other sources of internal noise, but also as a result of the variances associated with the two proportions that contribute to each d′ estimate. This second source, known as Bernoulli variance, causes the expected variance of d′ to vary a function of the true value of d′. Because estimates of d′ obtained from 2×2 matrices are discrete rather than continuous, the expected variance of the estimates cannot be specified by an equation. Miller [Percept. Psychophys. 58, 65 (1996)] has presented a method for computation of the sampling distribution of d′, for any true value of d′ and any given number of trials, and has demonstrated that a well-known approximation greatly exaggerates the variance for large values of d′. In the current paper, the standard approximation and Miller’s exact method are extended from Yes–No to the more commonly used 2IFC procedure and the effects of two standard corrections for zero cells are examined. A comparison of the theoretical results to actual data suggests that Bernoulli variance plays a greater role than internal noise in determining the variability in d′ estimates.