Superadditivity of the Ebbinghaus and Müller-Lyer illusions depends on the method of comparison used.

Illusions are useful tools for understanding fundamental visual processing. The method used to measure illusion strength is important but often neglected. We identified two methods of comparing bipart illusion elements (eg of the Müller-Lyer or Ebbinghaus illusions). For simultaneous adjustment an increase in size of one figure causes a decrease in the other. For independent adjustment one figure remains fixed while the other is adjusted to match it. These direct comparison illusion effects are contrasted to separate comparison illusion effects, where a neutral stimulus is matched to each illusory figure. If the illusion is stronger for direct comparisons, it is superadditive. The superadditivity of the Ebbinghaus illusion has been investigated using only simultaneous adjustment (Franz, Gegenfurtner, Bülthoff, & Fahle, 2000, Psychological Science 11 20-25), and the Müller-Lyer illusion using only independent adjustment (Gilster & Kuhtz-Buschbeck, 2010, Journal of Vision 10 (1):11, 1-13). Superadditivity was found for the Ebbinghaus but not the Müller-Lyer illusion, but this may have been due to the comparison method or differences between the illusions. Here we test both illusions with both methods of adjustment. Our results suggest that both illusions are superadditive for simultaneous adjustment, but for independent adjustment only under limited circumstances. Implications for research on illusions and perception and action are discussed.