Sensitivity within each motion direction was also estimated for each observer separately by
d′ from signal detection theory, a measure that is independent of observer bias (Green & Swets,
1966/1973). For a particular motion direction, we considered signal trials as those with light paths in the correct direction, and all remaining trials as non-signal trials. Therefore, we defined the hit rate for a particular motion direction,
p H, to be the probability of a correct motion classification, and the false alarm rate,
p F, to be the probability of classifying a trial as that particular motion direction when a different motion had occurred. If Φ
−1 is the inverse of the cumulative unit normal distribution, then
A zero value of
d′ indicates chance performance, and
d′ increases with increased discrimination performance. In our task, a
d′ = 1 corresponds to 69% correct,
d′ = 2 corresponds to 84% correct, and
d′ = 3 corresponds to 93% correct if a symmetric criterion is adopted. Ninety-five percent confidence intervals for each
d′ estimate were obtained by a non-parametric bootstrap method (Efron & Tibshirani,
1993): each observer's performance in the corresponding condition was simulated 100,000 times and the 5th and 95th percentiles were calculated and used to construct 95% confidence intervals.