32:, such as the weights of objects, and comparisons of the extremity of an attitude expressed within statements, such as statements about capital punishment. The measurements represent how we perceive entities, rather than measurements of actual physical properties. This kind of measurement is the focus of
996:
estimation. With this in mind, the specification of uniform discriminal dispersions is equivalent to the requirement of parallel Item
Characteristic Curves (ICCs) in the Rasch model. Accordingly, as shown by Andrich (1978), the Rasch model should, in principle, yield essentially the same results as
82:
and handwriting specimens, in pairs. He soon extended the domain of application of the law of comparative judgment to things that have no obvious physical counterpart, such as attitudes and values (Thurstone, 1929). For example, in one experiment, people compared statements about capital punishment
136:
Thurstone stated Weber's law as follows: "The stimulus increase which is correctly discriminated in any specified proportion of attempts (except 0 and 100 per cent) is a constant fraction of the stimulus magnitude" (Thurstone, 1959, p. 61). He considered that Weber's law said nothing directly
124:
the discriminal dispersions associated with stimuli are constant (as in Case 5 of the LCJ outlined below), then Weber's law will also be verified. He considered that the Weber-Fechner law and the LCJ both involve a linear measurement on a psychological continuum whereas Weber's law does not.
128:
Weber's law essentially states that how much people perceive physical stimulus intensity to change depends on that intensity. For example, if someone compares a light object of 1 kg with one slightly heavier, one notices a relatively small difference, perhaps when the second object is
108:. It represents a general theoretical model which, applied in a particular empirical context, constitutes a scientific hypothesis regarding the outcomes of comparisons between some collection of objects. If data agree with the model, it is possible to produce a scale from the data.
93:. For example, suppose that someone wishes to measure the perceived weights of a series of five objects of varying masses. By having people compare the weights of the objects in pairs, data can be obtained and the law of comparative judgment applied to estimate scale values of the
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1.2 kg. On the other hand, if someone compares a heavy object of 30 kg with a second, the second must be quite a bit larger for a person to notice the difference, perhaps when the second object is 36 kg. People tend to perceive differences that are
572:
Thurstone specified five particular cases of the 'law', or measurement model. An important case of the model is Case 5, in which the discriminal dispersions are specified to be uniform and uncorrelated. This form of the model can be represented as follows:
162:. Accordingly, from the point of view of Thurstone's approach, treating the JND as a unit is justifiable provided only that the discriminal dispersions are uniform for all stimuli considered in a given experimental context. Similar issues are associated with
120:, which are sometimes (and misleadingly) regarded as one and the same, are independent, in the sense that one may be applicable but not the other to a given collection of experimental data. In particular, Thurstone showed that if Fechner's law applies
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involve a physical stimulus, whereas the other 'laws' do. Another key difference is that Weber's law and the LCJ involve proportions of comparisons in which one stimulus is judged greater than another whereas the so-called Weber-Fechner law does not.
318:
137:
about sensation intensities at all. In terms of
Thurstone's conceptual framework, the association posited between perceived stimulus intensity and the physical magnitude of the stimulus in the Weber-Fechner law will only hold when Weber's law holds
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of such values. Thurstone (1959, p. 20) used the term discriminal process to refer to the "psychological values of psychophysics"; that is, the values on a psychological continuum associated with a given stimulus.
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in order to ascertain whether specific theoretical criteria for measurement have been satisfied. Some of the relevant criteria were articulated by
Thurstone, in a preliminary fashion, including what he termed the
169:
In addition, Thurstone employed the approach to clarify other similarities and differences between Weber's law, the Weber-Fechner law, and the LCJ. An important clarification is that the LCJ does not
86:
The essential idea behind
Thurstone's process and model is that it can be used to scale a collection of stimuli based on simple comparisons between stimuli two at a time: that is, based on a series of
1068:"Relative Measurement and its Generalization in Decision Making: Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors - The Analytic Hierarchy/Network Process"
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of measurement. Importantly, this is not simply given a priori (Michell, 1997, p. 355), as is implied by purely mathematical derivations of the one law from the other. It is, rather, an
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weights. This is the perceptual counterpart to the physical weight of the objects. That is, the scale represents how heavy people perceive the objects to be based on the comparisons.
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1001:. Like the Rasch model, when applied in a given empirical context, Case 5 of the LCJ constitutes a mathematized hypothesis which embodies theoretical criteria for measurement.
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to the size rather than noticing a specific difference irrespective of the size. The same applies to brightness, pressure, warmth, loudness, and so on.
1184:. In T.V. Smith and W.K. Wright (Eds.), Essays in Philosophy by Seventeen Doctors of Philosophy of the University of Chicago. Chicago: Open Court.
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is distributed according to some density function, such as the normal distribution or logistic function. In order to do so, it is necessary to let
47:, which is any process in which a comparison is made between pairs of a collection of entities with respect to magnitudes of an attribute, trait,
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question whether measurements have been obtained; one which requires justification through the process of stating and testing a well-defined
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Thurstone published a paper on the law of comparative judgment in 1927. In this paper he introduced the underlying concept of a
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When a simple logistic function is employed instead of the normal density function, then the model has the structure of the
24:. In modern-day terminology, it is more aptly described as a model that is used to obtain measurements from any process of
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of the Rasch model has been eliminated, as is achieved through statistical conditioning during the process of
Conditional
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Bradley, R.A. and Terry, M.E. (1952). Rank analysis of incomplete block designs, I. the method of paired comparisons.
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25:
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Krus, D.J., & Kennedy, P.H. (1977) Normal scaling of dominance matrices: The domain-referenced model.
313:{\displaystyle S_{i}-S_{j}=x_{ij}{\sqrt {\sigma _{i}^{2}+\sigma _{j}^{2}-2r_{ij}\sigma _{i}\sigma _{j}}},}
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In somewhat more technical terms, the law of comparative judgment is a mathematical representation of a
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Review of the Royal
Academy of Exact, Physical and Natural Sciences, Series A: Mathematics (RACSAM)
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Andrich, D. (1978b). Relationships between the
Thurstone and Rasch approaches to item scaling.
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is the sigma corresponding with the proportion of occasions on which the magnitude of stimulus
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How to
Analyze Paired Comparisons (tutorial on using Thurstone's Law of Comparative Judgement)
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29:
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Decision Making for
Leaders: The Analytic Hierarchy Process for Decisions in a Complex World
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Michell, J. (1997). Quantitative science and the definition of measurement in psychology.
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Thurstone showed that in terms of his conceptual framework, Weber's law and the so-called
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One important application involving the law of comparative judgment is the widely used
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for dichotomous data (Rasch, 1960/1980) is identical to the BTL model after the person
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28:. Examples of such processes are the comparisons of perceived intensity of physical
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theory the 'law' of comparative judgment is more aptly described as a measurement
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to judge which of each pair expressed a stronger positive (or negative) attitude.
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Although
Thurstone referred to it as a law, as stated above, in terms of modern
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can be inferred directly from the proportion of instances in which
984:(BTL model) (Bradley & Terry, 1952; Luce, 1959). In turn, the
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is the correlation between the discriminal deviations of stimuli
78:' involving the comparison between a series of stimuli, such as
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Probabilistic models for some intelligence and attainment tests
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is normally distributed, then it would be inferred that
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1042:. Pittsburgh, Pennsylvania: RWS Publications.
392:is judged to exceed the magnitude of stimulus
1152:: A Theoretical Analysis. New York: J. Wiley.
1191:. Chicago: The University of Chicago Press.
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1182:The Measurement of Psychological Value
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1171:A law of comparative judgement
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752:{\displaystyle {S_{i}-S_{j}}}
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1150:Individual Choice Behaviours
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1187:Thurstone, L.L. (1959).
1180:Thurstone, L.L. (1929).
1169:Thurstone, L.L. (1927).
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