The results described above suggest that both reflexive and voluntary saccades are modulated by changes in perceived target distance produced by the M-L illusion, but that the effects of the illusion are larger for voluntary movements. An additional analysis was conducted to rule out alternative interpretations of these data. One possibility is that these results are not evidence of a functional difference between voluntary and reflexive saccades, but were produced by differences in saccade latency. As noted, voluntary latencies were considerably longer than reflexive latencies. Results might therefore be taken to indicate not that reflexive saccades are less susceptible to illusion than voluntary saccades, but that short latency movements are less susceptible than long latency movements. A related possibility is that the seeming effect of the M-L illusion on reflexive saccade amplitudes might actually have resulted from voluntary movements occasionally produced in response to a visual go-signal. The distribution of saccade amplitudes produced in response to a visual go-signals, in other words, might have comprised a mixture of voluntary saccade amplitudes showing a relatively large effect of the illusion and reflexive saccade amplitudes showing no effect. This hypothesis, like the differential-latency hypothesis noted above, suggests that the effects of stimulus configuration on reflexive saccade amplitude should be larger for long-latency than for short-latency saccades.
An additional concern is that differential effects of wings-in and wings-out patterns on movement amplitudes might reflect a center-of-gravity tendency in saccade targeting (
Coren & Hoenig, 1972;
Findlay, 1982;
He & Kowler, 1989), rather than the influence of an illusory percept,
per se. Data would then indicate that reflexive saccades are more resistant to the center-of-gravity tendency than are voluntary saccades, but would not speak to the effects of illusion on oculomotor programming. Existing data cast doubt on this possibility; although center-of-gravity targeting appears to be the default strategy in eye movement programming, observers can easily target non-central positions within a shape when instructed to do so (
He & Kowler, 1991). It thus seems unlikely that a center-of-gravity tendency would have strongly influenced performance in the current experiment, where observers were instructed to target a specific and well-defined target position (the end of the horizontal stimulus shaft). Nonetheless, it is useful to seek additional evidence against the center-of-gravity hypothesis. Evidence indicates, notably, that center-of-gravity effects are modulated by saccade latency. More specifically, center-of-gravity effects are larger for short-latency saccades than for long-latency movements (
Coëffé & O’Regan, 1987;
Deubel, 1996;
Ottes, van Gisbergen, & Eggermont, 1985). The center-of-gravity account of the current data therefore predicts that the M-L illusion should affect short-latency movements more strongly than long-latency movements.
To examine these various possibilities, saccade amplitude data within each cell of the design were subjected to a median split on the basis of movement latency, and were reanalyzed with a 2 × 2 × 2 × 2 ANOVA that included saccade latency (below median vs. above median), saccade type, stimulus configuration, and saccade target distance as within-subjects variables. Consistent with the possibility that the influence of the illusion might vary with saccade latency, the analysis revealed marginally reliable interactions of saccade latency by saccade type by target distance [F(1, 7) = 5.196, p = .057, MSE = .067] and of saccade latency by saccade type by stimulus figure by target distance [F(1, 7) = 5.207, p = .056, MSE = .105]. Upon examination, however, these effects did not contradict any of the conclusions drawn above. For closer analysis, voluntary and reflexive movements were submitted to separate three-way ANOVAs with saccade latency, stimulus configuration, and target distance as factors. A reliable three-way interaction indicated that the effect of the M-L illusion on voluntary saccades was stronger for long-latency than for short-latency movements [F(1,7) = 7.464, p = .029, MSE = .119] with mean magnitude of the bias produced by M-L wings increasing from .58°, SE = .12, for saccades of below-median latency, to 1.05°, SE = .10, for saccades of above-median latency. Conversely, a nonsignificant three-way interaction within the reflexive saccade data [F(1, 7) = .205, p = .665, MSE = .005] suggested that latency did little to modulate the influence of the M-L illusion on externally triggered movements, with mean effect magnitude being .33°, SE = .08, for saccades of below-median latency, and .24°, SE = .05, for saccades of above-median latency. Thus, contrary to a center-of-gravity explanation, the influence of the M-L illusion did not tend to decrease as saccade latencies increased. Contrary to the possibility that differences in mean latency might account for the differential susceptibility of reflexive and voluntary movements to the M-L illusion, or that a small number of voluntary movements might have contaminated the reflexive saccade data, latency did nothing to modulate the influence of the illusion on reflexive saccades.