Categorical Judgment Scaling with Ordinal Assumptions

One of the most common activities of psychologists and other researchers is to construct Likert scales and then proceed to analyze them as if the numbers constituted an equal interval scale. There are several alternatives to this procedure (Thurstone & Chave, 1929; Muthen, 1983) that make normality assumptions but which do not assume that the answer categories as used by subjects constitute an equal interval scale. In this paper a new alternative is proposed that uses additive conjoint measurement. It is assumed that subjects can report their attitudes towards stimuli in the appropriate rank order. Neither within-subject nor between-subject distributional assumptions are made. Nevertheless, interval level stimulus values, as well as response category boundaries, are extracted by the procedure. This approach is applied to three sets of attitude data. In these three cases, the equal interval assumption is clearly wrong. Despite this, arithmetic means seem to closely reflect group attitudes towards the stimuli. In one data set, the normality assumption of Thurstone and Chave (1929) and Muthen (1983) is supported, and in the two others it is supported with reservations.