Abstract
(i) Conformance of responses to the Guttman structure with items of different difficulty operationalizing the continuum of a construct; (ii) the Guttman structure is cumulative and more or less difficult items reflect more or less of the construct on the continuum; (iii) the total score of a person reproduces the unique pattern of responses across all items; (iv) the Guttman structure reflects successful ordering of persons but is not measurement relative to a unit; (v) The Rasch model is a probabilistic Guttman structure.
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References
Bogardus, E. S. (1933). A social distance scale. Sociology and Social Research,17, 265–271.
Guttman, L. (1950). The basis for scalogram analysis. In S. A. Stouffer & others (Eds.), Measurement and prediction. New York: Wiley.
Further Reading
Andrich, D. (1985). An elaboration of Guttman scaling with Rasch models for measurement. In N. Brandon-Tuma (Ed.), Sociological methodology (pp. 33–80). San Francisco: Jossey-Bass.
Guttman, L. (1950). The problem of attitude and opinion measurement. In S. A. Stouffer & others (Eds.), Measurement and prediction. New York: Wiley.
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Exercises
Exercises
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1.
Organize the data from the Exercises in Chap. 3 in terms of a Guttman structure according to Table 5.5 in this chapter.
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2.
Draw a frequency distribution of the scores of the persons.
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3.
Organize the data in terms of a Guttman structure according to Table 5.6.
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4.
Calculate the discriminations for items 2, 5 and 7.
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5.
Draw the plots of the discriminations of items 2, 5 and 7 as in Fig. 5.1.
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6.
Which of these three items is the best discriminating item? Comment on the operation of each item.
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Andrich, D., Marais, I. (2019). The Guttman Structure and Analysis of Responses. In: A Course in Rasch Measurement Theory. Springer Texts in Education. Springer, Singapore. https://doi.org/10.1007/978-981-13-7496-8_5
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DOI: https://doi.org/10.1007/978-981-13-7496-8_5
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