Studies of magnitude scaling in the context of psychophysical measurement ha¨e
yielded se¨eral generalizations, which apply as well to the domain of attitude measure-
ment Ste¨ens, 1975.. i. There is a fair degree of agreement among observers on
the ratios of the magnitudes that they assign to the sensations evoked by particular
stimuli. ii. In the absence of a designated common modulus, there are large
individual differences in the mean values of judgments: some observers assign
generally high numbers to all stimuli, others assign low numbers. iii. The distribution
of responses to any stimulus is positively skewed; a log-normal distribution
often provides an adequate fit. iv. The standard deviation of the judgments of
different stimuli is approximately proportional to their means; this relationship
holds both when the same individual judges each stimulus several times and when
the judgments are contributed by different observers. In contrast, category scales
are characterized by a negligible correlation between the mean and the standard
deviation of judgments. v. In general, magnitude judgments of sensory intensity
are a power function of the relevant physical variable: for example, brightness is a
power function of luminance and loudness is a power function of sound amplitude
both with an exponent of approximately 1r3.. vi. Magnitude scales are generally
related by a power function to category scales of the same stimuli.
Studies of magnitude scaling in the context of psychophysical measurement ha¨eyielded se¨eral generalizations, which apply as well to the domain of attitude measure-ment Ste¨ens, 1975.. i. There is a fair degree of agreement among observers onthe ratios of the magnitudes that they assign to the sensations evoked by particularstimuli. ii. In the absence of a designated common modulus, there are largeindividual differences in the mean values of judgments: some observers assigngenerally high numbers to all stimuli, others assign low numbers. iii. The distributionof responses to any stimulus is positively skewed; a log-normal distributionoften provides an adequate fit. iv. The standard deviation of the judgments ofdifferent stimuli is approximately proportional to their means; this relationshipholds both when the same individual judges each stimulus several times and whenthe judgments are contributed by different observers. In contrast, category scalesare characterized by a negligible correlation between the mean and the standarddeviation of judgments. v. In general, magnitude judgments of sensory intensityare a power function of the relevant physical variable: for example, brightness is apower function of luminance and loudness is a power function of sound amplitudeboth with an exponent of approximately 1r3.. vi. Magnitude scales are generallyrelated by a power function to category scales of the same stimuli.
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