Computer Augmented Psychophysical Scaling

Abstract

Computer Augmented Psychophysical Scaling Robert L. West ( robert_west@carleton.ca ) Department of Psychology, Department of Cognitive Science, Carleton University, Ottawa, Canada Ronald L. Boring ( rlboring@ccs.carleton.ca ) Department of Cognitive Science, Carleton University, Ottawa, Canada Stephen Moore ( srmoore@chat.carleton.ca ) Department of Cognitive Science, Carleton University, Ottawa, Canada Abstract In this paper we present a methodology for improving the reliability of observers in magnitude estimation tasks by using the computer to augment the cognitive components of the task. Psychophysical scaling is the study of how to accurately measure perception. More specifically, the goal is to find methodologies that allow people to accurately communicate the magnitudes of specific dimensions of conscious experience, such as brightness, loudness, temperature, and heaviness. Psychophysical scaling can also be used for measuring the magnitude of subjective experiences such as level of happiness (e.g., West & Ward, 1988). The goal of psychophysical scaling is to find the mathematical functions that map the magnitudes of external stimulus dimensions to the conscious perception of magnitude. This enterprise is extremely useful for both scientific and applied research. Numerous different scaling techniques exist. However, our focus is on magnitude estimation, which is one of the most commonly used psychophysical methods. Magnitude estimation (ME) was invented by Stevens (1956) and involves exposing subjects to a set of stimuli and asking them to match the magnitude of a particular dimension of each stimulus to the magnitude of a number. This is repeated for multiple trials to provide multiple responses for each stimulus value. To avoid the influence of outliers, the median or the geometric mean of the responses for each stimulus value is calculated. Numerous studies have shown that plotting these values against the stimulus values produces functions that are closely approximated by power functions. This is known as, the Power Law, or, Stevens’ Law. The form of the power law is, R=KS B , where R is the observer’s response, S is the stimulus magnitude, B is the exponent value, and K is a constant. Logging both sides of the equation produces, Log(R)=B⋅Log(S)+Log(K), which is a straight line with B estimated by the slope and K by the intercept. The exponent, B, can be interpreted as a metric for stimulus compression. This reflects the fact that people use a power function or something closely approximating a power function to compress stimuli, just as audio and video files can be compressed to save on bandwidth. In fact, audio and video compression go unnoticed to the extent that the compression function maps onto the human compression function for the same stimuli. Generally speaking, in ME the goal is to put as few restrictions on the observer’s choice of numbers as possible. Often free ME (e.g., see Zwislocki & Goodman, 1980) is used, in which observers are instructed to match the perceived magnitude of the stimulus to whatever number seems most natural. This is quite different from the common psychological practice of imposing scales on people. The reasons for this are both theoretical and practical. From a mathematical standpoint, if any two stimuli are set equal to any two responses then you have determined what the exponent value must be. Thus, if an observer uses the lowest value on a scale to match the lowest perceived magnitude and the highest value to match the highest perceived magnitude, the power function exponent has been fixed. To get around this one could assign a value to a middle value on the scale and not impose a top end or bottom end, but this has been shown to produce confusion and poor results (Stevens, 1975). However, the fact that peoples’ backgrounds cause them to use different ranges of numbers in their responses is not a problem as these differences are captured by the K constant (since response range is usually not of interest, K values are usually not reported). ME can be considered a special case of cross modal matching (CMM). In cross modal matching, the observer adjusts the magnitude of one stimulus dimension to match the magnitude of another stimulus dimension (e.g., adjusting the brightness of a light to match the loudness of a tone). Like ME, CMM results also produce power functions. Furthermore, ME and CMM results are consistent in that they can be used to predict each other (e.g., the ME exponents for brightness and loudness can be used to predict the exponent relating brightness and loudness in a CMM experiment). Also, both the power functions and the specific exponent values found through ME are consistent with ratio scaling experiments, in which magnitude scales are derived by asking observers to set or report ratios between stimuli. These approaches to scaling are known as direct scaling techniques (Stevens, 1971). Problems ME forms the foundation for a potentially accurate and consistent way of measuring perceived magnitude. However,