In previous studies, judgments of ratios and differences in subjective magnitude have yielded similar orders, consistent with a hypothesis that a single perceived relation underlies both judgment tasks. In the present research, 15 subjects estimated heaviness differences between 28 pairs of eight weights and each of 8 groups of 10 subjects evaluated heaviness ratios of eight variable stimuli with respect to a different standard stimulus. Presenting stimuli that were equally spaced on a cube-root scale of weight enhanced expected ordinal discrepancies between ratio and difference estimates, and employing independent groups for each standard stimulus in ratio estimation eliminated a possible bias due to varying standards within the presentation sequence. Differences in orders of ratio and difference estimates together with differences in scales obtained from non-metric analyses in terms of a difference model indicated that the judgments were based on two perceived relations that are ordinally consistent with arithmetic operations of ratios and differences. A ratio scale of heaviness was derived from the combined orders of subjective ratios and differences.

Judged magnitudes of difference in area of paired circles and magnitude estimations of the circles making up the pairs were obtained from 11 5s. The difference judgments were subjected to nonmetric scaling, and a one-dimensional solution was obtained. The relationships between scale values and physical area and between judged difference and derived distance were each characterized by power functions. The product of exponents from the two functions closely predicted judgments of individual circles. Judgments of differences between paired weights were subjected to the same analysis. The relationships between scale values and physical weight and between judged difference and derived distance were power functions for both pooled data and data from individual 5s, indicating that input and output transformations in magnitude estimation are power functions.

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The relation between monocular and binocular brightness was examined. Clear evidence was found that the interaction between visual channels in binocular processing of brightness information implicates both an apparent averaging of monocular brightness when they are grossly different and a partial summation when they approach equality. A vector-sum model is shown to predict these properties. A nonmetric method was used to fit such a model to data from three experiments in each of which 15 subjects estimated brightness of binocularly fused targets. Magnitude estimation was used in two experiments, and cateogry ratings were obtained in the third experiment. When it was assumed only that subjects' responses were monotone with perceived brightness, estimates of the model's parameters from the data of the three experiments were almost identical, indicating that results from magnitude estimati;n and category rating can converge once nonlinear response functions are eliminated.

Four groups of 20 subjects each made magnitude judgements of either length or numcrousness either with a designated modulus or with freedom to select their own modulus. After a logarithmic transformation of the data from each subject, a residual measure was computed as ihe deviation of a response to a stimulus from the average of all responses to that stimulus. The residuals on successive presentations were found to correlate positively. They were also found to be related to their serial position within the presentation sequence. The results indicate a tendency for subjects to change the unit of their numerical estimates during the judgement sequence. Implications of sequential response effects for estimates of the exponent of the psychophysical power function were discussed. KKSUMK Quatrc groupes de 20 sujcts chacun faisaicnt des jugements dc longueur ou dc nombre soil avec un module designc ou avec la libcrtc de seleclionncr leur propre module. Aupres une transformation logurithmique des donnees pour chaque sujet, unc mesure residucllc ctait calculee comme la deviation dc la reponse a un stimulus par rapport la moyenne de toutcs Ics rcponses a cc stimulus. Les residuelles sur des presentations successives corrclaienl positivement. Elles etaient aussi reliees a leur position serielle dans la sequence de presentation. Les resultats indiquent unc tendance pour les sujcts a changer ('unite dc leurs eslime's numcriques pendant la sequence de jugement. Les implications des effeis de reponse sequentiellc pour des estimes de l'cxposanl de la puissance de la fonction psychophysique sont discutees.