Threshold Determination by Titration: A Markoff Chain Model

Threshold is often defined as that stimulus intensity which is correctly detected 50% of the time. A titration procedure increases the stimulus intensity by a fixed increment if the subject fails to detect the stimulus, and decreases the stimulus if it is detected. The mean stimulus intensity thus obtained is an estimate of threshold. The Markoff chain model developed here allows the mean and variance of the mean to be calculated for any specified stimulus values, number of trials, and distribution of the underlying variate. Examples are given to illustrate the effects of changing the experimental parameters and the underlying distribution. The titration mean was fairly insensitive to these changes.