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A note examines psychophysical scales and their mathematical foundations, suggesting multidimensional approaches.
On viewing Thurstone's psychophysical scale from the point of view of the mathematical theory of one-parameter continuous groups, it is seen that a variety of different psychological or statistical assumptions can all be made to lead to a scale possessing similar properties, though requiring different computational techniques for their determination. The natural extension to multi-dimensional scaling is indicated.
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Young et al. (1941) studied this question.
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