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The Measurement of Sensation$
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Donald Laming

Print publication date: 1997

Print ISBN-13: 9780198523420

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198523420.001.0001

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Why Stevens' Law is a power law

Why Stevens' Law is a power law

(p.168) 11 Why Stevens' Law is a power law
The Measurement of Sensation

Donald Laming

Oxford University Press

This chapter explains why Stevens' Power Law is a power law, rather than some other kind of relation. If the stimulus values are chosen in a geometric series and participants are induced to judge ratios — that is, to distribute their responses on a logarithmic scale — the great variability of magnitude estimates means that linear regression of log numerical estimate on log stimulus magnitude is the only meaningful relationship to emerge from the experiment. The power law exponent is chiefly determined by the range of the physical variable in relation to the approximately uniform range of numbers used by Stevens' participants. The uniformity of that range is enhanced by instructions. The value of the exponent is, however, modified by prior expectations, which generate a small but systematic difference between the exponents estimated from magnitude estimation and production.

Keywords:   instructions, judging ratios, linear regression, magnitude estimation, magnitude production, number range, power law exponent, prior expectations

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