The slope of psychometric functions as an estimator of intrinsic temporal noise

The interpretation of threshold curves and internal signals derived from them is often hampered by probability summation, i.e., the contribution of internal noise to detection. It will be shown that starting from a few plausible assumptions its effect can be calculated provided the strength parameter of the intrinsic noise is known. Its value can be derived from the slope of the psychometric function. The best way to obtain an unbiased precise estimate is rather controversial. We advocate pooling slope-data obtained by fast measurement using small samples. If the slope is then estimated by maximum likelihood, this will result in a positive bias as reported by several authors. However, Monte Carlo experiments have shown that other methods of estimation based on weighted linear regression give results that are practically unbiased. In the case of a logistic distribution the bias of the M-L estimator is proved analytically