A Correlational Analysis of Symmetry between the Arrowhead and Featherhead Müller-Lyer Illusions

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Abstract
Correlational methods were used to investigate symmetry of effect for the arrowhead and featherhead versions of the Müller-Lyer figure. Two control figures were compared in the determination of baseline levels for measurement of the illusions: a shaft presented without any inducing context, and a shaft with vertical inducing lines attached. In addition, results based on difference-score measures of the illusions were contrasted with results obtained by partial-correlation techniques. Overall, when one considers the results for either one of the arrowhead or featherhead versions, the evidence favours a common underlying mechanism. However, results across the two versions suggest that the mechanisms for the two versions differ fundamentally. In weighing the different kinds of evidence contributing to this conclusion, methodological issues were raised. By obtaining two judgments for each stimulus figure from a large number of subjects, it was possible to demonstrate not only that conventional difference-score measures of illusions are highly unreliable, but also that they can yield biased results.