Modern psychophysical theory was born with the 1860 publication of Gustav Fechner's monumental Elements of Psychophysics. A cornerstone of this work was Fechner's extension of the Gaussian Theory of Error to the comparison of sensations. Thus, among his many other contributions, Fechner was the first to account for trial-by-trial variability in the sensory effects of a stimulus. According to this view, the appropriate psychological representation is probabilistic. In 1927, L. L. Thurstone ( 1927a, 1927b, 1927c) published a series of papers that elaborated on Fechner's ideas about probabilistic representation and extended them to the fields of test theory and attitude measurement.
Among the best known and most successful modern theories to incorporate the assumption of probabilistic stimulus representation is Signal Detection Theory (e.g., Green & Swets, 1974). Besides incorporating the assumption that the sensory effects of a stimulus are probabilistic, Signal Detection Theory elaborated on Fechner's ideas about decision processes. Specifically, Signal Detection Theory assumed that the detection process could be separated into two components: sensory and decision. The output of the sensory process was assumed to be the particular sensory value on that trial. The decision process was assumed to use the sensory value and the experimenter's instructions to select a response.
Models incorporating probabilistic representation were hugely successful and are now studied in one form or another by virtually every graduate student in Experimental Psychology (most often in the form of Signal Detection Theory or Factor Analysis). The effect of this probabilistic approach on the areas of perception and cognition has been limited however, for one very important reason. With only a few exceptions, probabilistic models have assumed unidimensional psychological representations. Therefore, they work best when the stimulus var-