Integration theories and self-rating : the application of cognitive algebra to schema theory

An experiment was conducted to investigate the appropriateness of Anderson's (1981) averaging integration model to self-rating. This model would enable simultaneous estimation of the extremity (or position) and importance (or weight) of those self-schemata involved in a given rating task (Markus, 1977). It was hypothesised that the averaging model of integration could be described geometrically as predictive of a \city-block\" metric such that estimates of proximity (self-descriptiveness of adjective-qualifier pairs) consist of summed estimates of the proximities of each component of the stimulus item to a constant comparitor point. Geometrically this model therefore predicts that movement through the space in which rating takes place is horizontal and vertical but never diagonal. This model is contrasted with a euclidean metric in which ratings are predicted from the square root of the summed squared proximities. Stimulus items consisted of pairs of adjectives each qualified by one of six adverbs.There were two Adjective Type conditions (Abstract Concrete) and three Instructional Sets yielding a 6 (qualifier of first adjective) X 6 (qualifier of second adjective) X 2 (adjective type) within-subject factorial design with Instructional Set as a between groups factor. Data were visual-analog ratings from 0 (not at all like me) to 100 (exactly like me). These were subject to a range of model fitting procedures intended to 'identify convergence with the averaging and euclidean models including Median Polish (Tukey 1975) IMSL iteration procedures and residuals ANOVA (Anderson 1982). Results indicate that neither the averaging nor the euclidean models satifactorally predicted the ratings obtained as the data departs significantly from each. Of the two models however the euclidean model shows superior fit to the data. It is suggested that the results may be consistent with a differential-weight averaging model (Anderson 1982) although evidence to his conclusion is secondary."