Transmitted information and the length of rating scales.

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Abstract
Two studies are reported applying information theory to rating scales. In the first study rating scales with 2, 3, 5, 7, and 9 categories were used by 236 Ss to rate preference values of 20 foods . The information transmitted by each scale length was computed. Transmitted information showed a significantly high correlation with the logarithm of the number of scale categories. It was concluded that the amt. of information actually transmitted by a rating scale is a constant fraction of the max. amt. that could be transmitted under noiseless conditions. The second study checked this relationship when the input to the rater are stimulus lists varying in stimulus information. Three lists of ten foods were rated by 279 Ss using 2,3,4, or 5 category rating scales. Foods for each list were selected so as to vary the heterogeneity of stimuli on each list. Information measures were computed and equations relating Transmitted Information (It) and Maximum Response Information (log R) found for each list. The obtained equations (a) showed a rectilinear positive relationship between It and log R, (b) did not vary significantly in their slopes or rate of increase, and (c) demonstrated a positive relation between the magnitude of equation constants and the stimulus heterogeneity of the lists.
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