Representations for biased numerical judgments

Models are presented that introduce bias parameters into the numerical representations for ratio and interval judgments. An interval bias model is considered that has the capability of accounting for both interval and ratio judgments. A contrasting ratio bias model—a simple generalization of the classical model that accepts ratio judgments at face value—is also considered, and both models are tested with brightness data. The ratio estimation data lead to the conclusion that the constraints placed on the structure of the data by the classical model are too strong. In terms of goodness-of-fit and certain theoretical criteria, the interval bias model accounts for the ratio estimation data better than the ratio bias model. The interval estimation data are supportive of recent efforts directed toward the development of direct interval scaling theory.