Krus, D. J. & Kennedy, P. H. (1981) The misplaced illusion? The case of the Mueller-Lyer perceptual incongruity figure. Educational and Psychological Measurement, 41, 175-180.

The misplaced illusion? The case of the Mueller-Lyer perceptual incongruity figure.

David J. Krus and Patricia H. Kennedy
Arizona State University

Abstract. - Development or the computer-based analogue to the Mueller-Lyer apparatus was described along with the significance of this perceptual illusion figure to the history of psychometrics.

The authors first encountered the Mueller-Lyer apparatus at the University of Muenster, Germany, where the contraption was located in a rather dusty display window. Mounted on a dark brown oak board, its movable arrow was operated by a pair of worn out strings. It looked quite like the picture in Guilford’s (1936) Psychometric (Figure 1).

Figure 1. The Mueller-Lyer Apparatus. Reproduced by permission of McGraw-Hill Book Co., Inc., from J. P. Guilford’s Psychometric Methods, 1936, p. 26.

Feelings of respect and curiosity were heightened by the surroundings. Muenster is an old Hanseatic city. The medieval walls of its university still echo the footsteps of mendicant friars and Goliardic verses perpetuated by its early student body. Nevertheless, as the investigators later remembered, this encounter with the real Mueller-Lyer apparatus was disquieting.

Prior to visiting Germany, the authors must have seen hundreds of Mueller-Lyer figures in numerous styles and surprising variety of arrangements: horizontal and vertical, aligned on a line or separated by white space, with parallel or shifted edges (Figure 2).

Figure 2. The Mueller-Lyer Illusion. Reproduced by permission of Houghton Mifflin Co., from N. Munn et al. (1972) Introduction to Psychology, p. 174.

Some were printed in black and white; others were colored or redesigned by a graphic artist (Figure 3), but all were static and immovable, petrified in two-dimensional paper fields, never built in space like the original.

Figure 3. Photographic interpretation of the classical Mueller-Lyer illusion. Figure adapted by permission of Knopf, Inc. from D. Krech et al. (1969) EIements of Psychology, p. 162.

Interpretation of the meaning of the said illusion, as culled from numerous introductory psychology textbooks, varied from simplistic to sophisticated: On one side there were generalities of the Gestalt psychology such as that the whole is more than a sum of its parts. Somewhere in between were statements about “civilized” people of the rectangular “carpentered world” and “primitive” people of the oblique world of thatched huts and hogans. Hard to classify were findings that even chickens react in a manner which suggests that they experience an illusion and the continuum was capped by epistemological speculations such as Bishop Berkeley’s on whether esse est percipi  or not. Long forgotten were issues connected with this venerable figure which helped to shape the quantitative world of psychologists: The exciting discoveries of Steinheil and Laugier, equating variable lighted surfaces to the brightness of stars which with Bessel’s formulation of the personal equation problem led Fechner to consider the problem of constant and variable errors within the framework of the Mueller-Lyer apparatus (Fechner, 1882, Muller, 1878); the link between Fechner’s (1882) psychophysical method of average error and Spearman’s (1907, 1910) formulation of the theory of true and error test scores; the conceptual necessity of Fechner’s separation of constant errors (experimental treatments) from their error components as a conditio sine qua non of the subsequent developments in the area of experimental design. To attract students to this “psychometric connection” it was decided to simulate the Mueller-Lyer apparatus by using Terak 8510 graphic computer.

Retrospect and Prospectus

Perusing relevant yellowed pages of old manuscripts, the authors observed that successive eras each assigned their Zeitgeist-colored interpretations to Mueller-Lyer illusion figure. Early pioneers regarded the method of average error, encompassed by the Mueller-Lyer illusion as a clue to the quantitative solution of the “mind-body” problem (Titchener, 1905); a problem launched by La Mettrie, Cabanis, and Descartes and reverberating throughout centuries into the age of Ashby, Wiener, and Von Neumann. At the turn of the century, psychometricians built the classical test theory around Fechner’s concept of normal and error distances, as reflected in the elegant formulation of the theory of true and error test scores.

The computerized illusion fared better in many ways than the original apparatus. Easily portable, it was housed on a floppy disc instead of an oak board. It avoided the “motor errors” of Muller (1818, p. 80) and “errors of movement” of Fullerton and Cattell (1892, p. 111) caused by the “uncertainty of the hand.’ Yet one wondered, had the Mueller-Lyer illusion replete with its historical connections been restored to its rightful place, or had a new illusion been created, or did it matter.

References 
Fechner, G. T. (1882) Revision der Hauptpunkte der Psychophysik. Leipzig: Breitkopf und Hartel.
Fullerton, G. S. and Cattell, J. McK. (1892) On the perception of small differences. Philosophical Series, 2, 1-120.
Guilford, J. P. (1936) Psychometric methods. New York: McGraw-Hill.
Leibniz, G. W. (1677, 1924) Zur Allgemeinen Characteristik. In A, Buchenau and E. Cassirer (eds.) Leibniz Philosophische Werke. Leipzig,Germany, pp. 184-189.
Leibniz, G. W. (1679, 1903) Principia calculi rationlis. In L. Couturat (ed.) Opuscules et fragments inedits de Leibniz. Paris, France, pp. 229-231.
Muller, G. E. (1878) Zur Grundlegung der Psychophysik. Berlin, Germany: T. Griefen.
Spearman, C. (1907) Demonstration of formulae for true measurement of correlation. American Journal of Psychology, 18, 161-169.
Spearman, C. (1910) Correlation calculated with faulty data. British Journal of Psychology, 3, 271-295.
Titchener, E. B. (1905) Experimental psychology. New York: Macmillian.