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Test of a Multiplying Model for Estimated Area of Rectangles

1971; University of Illinois Press; Volume: 84; Issue: 4 Linguagem: Inglês

10.2307/1421171

1939-8298

Norman H. Anderson, David J. Weiss,

Ergonomics and Musculoskeletal Disorders

Graphic ratings of physical size were obtained for 36 rectangles in a 6 X 6, width x height design, with each factor ranging from 3 to 18 cm. These judgments were approximately linear in physical area and followed a multiplying model reasonably well, though not perfectly. It is suggested that the underlying process was one of additive integration and that functionalmeasurement procedures can be used to scale phenomenal size of complex shapes. Previous work on judgments of area has been largely concerned with accuracy, and with the relation between the response and the physical area (Ekman and Junge, 1961; Stevens and Guirao, 1963; Teghtsoonian, 1963; Stanek, 1969). This orientation toward the physical stimulus measure has tended to pass over the psychological processes involved in area judgments. The importance of a process orientation is suggested by reports that judged area appears to be affected by shape as well as by physical area (Luckiesh, 1922, p. 97; Warren and Pinneau, 1955; Smith, 1969). An interesting example is cited by Paterson and Tinker (1938; see also Helson and Bevan, 1964; Tolansky, 1964, p. 49), who noted that, contrary to appearances, the marginal white space on a printed page is roughly equal to the central printed area. In a typical page of text in this journal, for example, the marginal area occupies approximately 44% of the page. The experiment reported here was designed to test a simple multiplying model for area of rectangles. The judged area was assumed to be, in effect, the product of the subjective values of width and height. A novel feature is the use of procedures from the theory of functional measurement (Anderson, 1970), procedures which test the model while allowing for subjective values of width and height. In this theory, no a priori assumption about the relation between subjective and objective stimulus values is needed. Differential weighting of the two stimulus dimensions is also allowed for, though this cannot be explicitly tested in a simple multiplying model.