Weighing the anchor in categorization of sound level
Keywords:Approximation theory, Computer simulation, Information analysis, Integral equations, Mathematical models, Matrix algebra, Random processes, Mathematical theory, Stimulus-response matrix
AbstractCategorization of sound level requires that the subject classify the intensity of stimulus tones into appropriate response categories. Intensities are selected at random from a fixed stimulus range and stimulus-response pairs are tabulated into a stimulus-response matrix. "Anchor" or edge effects are well-recognized phenomena by which tones selected from the extremities of the stimulus range are classified with greater accuracy than tones in mid-range. Observation reveals that data in the center rows of a matrix follow a typical normal error distribution, while data in extreme rows follow a heavily skewed distribution with smaller variance. We propose that the distribution of responses along all rows of the stimulus-response matrix is described by a single, underlying normal density of constant variance. We develop the mathematical theory for extracting this constant underlying variance, ?2, from an experimental "parent" matrix. A set consisting of all possible matrices (including the parent matrix) with core variance, ?2, and containing the usual anchor phenomena, can then be generated at will. Using this core variance, we derive an expression for the transmitted information, It, that comprises a non-anchor and anchor contribution, whereby the size of the anchor effect may be quantified. Essentially, we provide a method for removing anchor effects and revealing the single core variance that represents, by hypothesis, the stimulus-response matrix.
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