### Weighing the anchor in categorization of sound level

#### Abstract

Categorization 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, σ

^{2}, from an experimental "parent" matrix. A set consisting of all possible matrices (including the parent matrix) with core variance, σ^{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.#### Keywords

Approximation theory; Computer simulation; Information analysis; Integral equations; Mathematical models; Matrix algebra; Random processes; Mathematical theory; Stimulus-response matrix

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