unfolding technique

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A method of scaling a set of stimuli without relying on any presupposed scale of measurement. Imagine a set of stimuli that are statements about capital punishment (Capital punishment is never justified, People who commit murder should pay with their own lives, and so on) arranged along a hypothetical scale, with anti-capital-punishment statements near the left and pro-capital-punishment statements near the right. Suppose an individual has judged the stimuli by the method of paired comparisons and produced the rank-ordering of them, from anti-capital-punishment to pro-capital-punishment, and suppose that the judge's ideal point—in this example, the point corresponding to the judge's own attitude towards capital punishment—is marked on the scale with an X, yielding a joint continuum or J scale. An example of a hypothetical J scale with the positions of five stimuli (statements about capital punishment) A, B, C, D, and E, and the individual's ideal point X, might be as follows:---A-----X---C--------B------------D--------E---From such a J scale, the individual's I scale could be obtained by imagining the J scale folded about the point X, so that the part of the scale to the left of the X is made to overlap the part to the right, yielding the following I scale:X---C--A--------B--------------D--------E---Reading from the X at the left, it is now clear that the individual's preference ordering of the five stimuli (attitude statements) is CABDE. If X had been closer to A than to C on the J scale, then the individual's preference order would have been ACBDE, and if X were to the right of the midpoint between C and B, then the order would been BCADE. Any I scale may thus be viewed as a folded J scale, and from empirical data consisting in effect of observed I scales, J scales may therefore be recovered by unfolding the observed I scales. By unfolding the I scales of a number of judges who have ranked the five stimuli (statements), each with a different ideal positions X on the hypothetical J scale, it is possible to infer not only the order of stimuli on the J scale, but also information about relative distances between them, and hence interval scale information can be inferred from purely ordinal scale input data, provided the judges behave consistently. For example, because the J scale depicted above induces the I scale CABDE and not CBADE, we can infer that the distance between A and C is less than the distance between C and B, although the data are purely ordinal. The technique was formulated by the US psychologist Clyde Hamilton Coombs (1912–88) and published in the journal Psychological Review in 1950, and is also called the Coombs unfolding technique. See also attitude scale, conjoint measurement theory, portfolio theory.

Subjects: Psychology.

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