The Random Step Method for Measuring the Point of Subjective Equality

Abstract

Points of Subjective Equality (PSE) are commonly measured using staircase or constant stimuli methods. However, the staircase method is highly dependent on the step size, and the constant stimuli method is time-consuming. Thus, we wanted to develop an efficient and quick method to estimate both the PSE and the slope of the psychometric function. We developed a random-step algorithm in which a one-up-one-down rule is followed but with a random step size in a pre-defined range of test levels. Each stimulus would be chosen depending on the previous response of the subject. If the subject responded “up”, any random level in the lower range would be picked for the next trial. And if the subject responded “down”, any random level in the upper range would be picked for the next trial. This procedure would result in a bell-shaped distribution of the test levels around the estimated PSE, while a substantial amount of trials would still be dispersed at both bounds of the range. We then compared this method with traditional constant stimuli procedure on a task based on the Pulfrich phenomenon while the PSEs of participants could be varied using different neutral density filters. Our random-step method provided robust estimates of both the PSE and the slope under various noise levels with small trial counts, and we observed a significant correlation between the PSEs obtained with the two methods. The random-step method is an efficient way to measure the full psychometric function when testing time is critical, such as in clinical settings.