In the recent literature on microsaccades and attention, two questions have been conflated. There is a broad question of whether microsaccades are related to attention, and there is a more specific question about whether microsaccades serve as an index of attention. We are happy to agree that microsaccades are related to attention. However, the claim that ‘‘microsaccades are an index of covert attention’’ (in the title of Laubrock, Engbert, Rolfs, & Kliegl, 2007, this issue) depends on a strong correlation. Were this claim true, a researcher might be able to conduct a study relying entirely upon microsaccade direction as a measure of attentional deployment. Although we would be delighted to be able to conduct such an experiment, both our data and those of Laubrock et al. suggest that microsaccades cannot be used as a reliable marker of covert attention. Laubrock et al. make two arguments. First, reviewing our experiment (Horowitz, Fine, Fencsik, Yurgenson, & Wolfe, 2007, this issue), they criticize our selection of trials on which the directions of the cue and microsaccade disagreed, arguing that this selection would inevitably lead to a negative microsaccade-congruency (MC) effect. Second, they report new data demonstrating a correlation betweenMC and reaction time (RT). We deal with these points in reverse order. Laubrock et al. have demonstrated a statistically reliable relationship between MC and RT. An incongruent microsaccade was associated with a 6-ms slowing of RT. This is a weak effect, an order of magnitude smaller than the 81-ms effect associated with an invalid cue. This effect may be statistically significant, but it suggests that microsaccade direction provides very little useful information about the spatial distribution of attention. Also, Laubrock et al. argue, under a seemingly reasonable set of assumptions, that in our study, trials on which the microsaccade direction diverged from the cue direction were dominated by trials on which the microsaccade did not follow attention, even if microsaccades usually did follow attention. The argument is as follows. Assume that observers direct attention toward the cue with probability w, and that the microsaccade reflects the direction of attention with probability x. Let v denote cue validity. There are two kinds of trials on which the cue is valid but the cue direction and microsaccade direction disagree: (a) valid trials (v) on which attention does not follow the cue (1 w) and the microsaccade follows attention (x) and (b) valid trials (v) on which attention follows the cue (w) but themicrosaccade does not reflect attention (1 x). The proportion of trials of the first type is given by p15 v(1 w)x, and the proportion of trials of the second type is given by p25 vw(1 x). Laubrock et al. note that if w5 v and x5 .75 (i.e., the microsaccade is almost as good an index of attention as the cue), the predictions would be qualitatively consistent with our results. However, this scenario is not quantitatively consistent with our results. Although w and x are not directly observable, one can observe the proportion of trials on which the cue direction and microsaccade direction disagree, p5 p1 1 p2 5 v(w1 x 2wx). Because v is known (arrow cues were 80% valid, so v 5 .80), any observed p is compatible with a line through wx space. Figure 1 plots the wx curves that could produce the observed ps in the manual-detection condition of our experiment for all 3 observers (data from the other two conditions lead to similar conclusions). The diamond represents the hypothetical point on which Laubrock et al. base their argument (w 5 .80, x 5 .75); this point is clearly not consistent with the data. In fact, if we assume that observers frequently shifted attention in the direction of the cue (i.e., w .60), then the probability that the microsaccade followed attention must have been less than .55 (note that if x 5 .50, then the direction of the microsaccade is independent of attention). If observers were at least probability matching (i.e., w .80), then x would have been less than .52. Thus, the predictive power of microsaccades is, for practical purposes, negligible. Address correspondence to Todd S. Horowitz, Visual Attention Laboratory, Brigham and Women’s Hospital, 64 Sidney St., Suite 170, Cambridge, MA 02139, e-mail: toddh@search.bwh.harvard.edu. PSYCHOLOGICAL SCIENCE
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