Formulas for Equating Ratings on Different Scales

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Abstract
Formulas for transforming scores and statistics on a rating scale having any number of categories to a scale having a different number of categories are described. The origins of the two scales may be any negative or positive integers; the scales may increase in the same or opposite directions and have any category widths. The transformation formulas provide not only a procedure for equating scores on different scales but also a method of investigating a variety of research questions involving ratings. To illustrate the use of one of the formulas, the means and variances of 10 items on six forms of a course evaluation questionnaire were compared. Significant differences were found in transformed mean item ratings for some of the six forms, which differed in the number of categories (2, 3, 4, 5, 6 or 7) available to the raters.

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