It is still a matter of debate whether observers can attend simultaneously to more than one location. Using essentially the same paradigm as was used previously by N. P. Bichot, K. R. Cave, and H. Pashler (1999), we demonstrate that their finding of an attentional “split” between separate target locations only reflects the early phase of attentional selection. Our subjects were asked to compare the shapes (circle or square) of 2 oddly colored targets within an array of 8 stimuli. After a varying stimulus onset asynchrony (SOA), 8 letters were flashed at the previous stimulus locations, followed by a mask. For a given SOA, the performance of subjects at reporting letters in each location was taken to reflect the distribution of spatial attention. In particular, by considering the proportion of trials in which none or both of the target letters were reported, we were able to infer the respective amount of attention allocated to each target without knowing, on a trial-by-trial basis which location (if any) was receiving the most attentional resources. Our results show that for SOAs under 100–150 ms, attention can be equally split between the two targets, a conclusion compatible with previous reports. However, with longer SOAs, this attentional division can no longer be sustained and attention ultimately settles at the location of one single stimulus.

- attention was preferentially allocated to target locations over distractor locations;
- given that a letter at a target location was reported, the other target location still enjoyed a greater letter report probability than distractor locations;
- letter report at distractor locations intervening between the two targets was not better than at other distractor locations.

*a*

_{ n}

*x*

^{ n}+

*a*

_{ n−1}

*x*

^{ n−1}+

*a*

_{ n−2}

*x*

^{ n−2}+ …. +

*a*

_{0}= 0, with

*a*

_{ n}≠ 0, the sum of the roots is −

*a*

_{ n−1}/

*a*

_{ n}and the product of the roots is

*a*

_{0}/

*a*

_{ n}if

*n*is even, and −

*a*

_{0}/

*a*

_{ n}if

*n*is odd. From this theorem and Equations 3 and 4, P(T1) and P(T2) are the solutions of the following second-degree equation:

*t*-test. If Δ is significantly positive (

*p*< 0.05), the equal attentional split interpretation cannot hold any more.

*T*+

*ɛ*

_{1}and P(T2) =

*T*+

*ɛ*

_{2}, where

*T*is the true probability of detecting a target and

*ɛ*

_{1}and

*ɛ*

_{2}are normally distributed error terms across subjects. The true means of P(T1) and P(T2) are the same, implying that attention is equally allocated to the two targets (in other words, Δ = 0). For each subject, however, our method estimates two probability values and always assigns the greatest to P(T1). The final mean estimates of P(T1) and P(T2) across subjects will thus artificially differ, even though they are drawn from distributions with the same mean. Therefore, we always refer to the distribution of Δs first, before making any conclusions regarding P(T1) and P(T2): even when the mean values across subjects of P(T1) and P(T2) significantly differ, the hypothesis of an equal split of attention can only be rejected when Δ is significantly positive.

*ɛ*

_{1}and

*ɛ*

_{2}); the estimates will be more reliable and less susceptible to the above-mentioned bias, providing a less misleading picture than the mean of individual estimates (with the obvious caveat that no estimate of inter-subject variability can be computed in this case). In the following, we analyze and report both the pooled data and the means of individual values across subjects.

*between*targets should be greater than at distractor locations

*outside*of targets.

^{19}

_{2}). The total number of three-letter reports is (

^{20}

_{3}). Hence, the probability for that subject to report a letter by chance is on average (

^{19}

_{2}) / (

^{20}

_{3}) = 0.15 (the same calculation applied to the 7-SOA group, for which only 16 letter choices were given, would yield a chance level of (

^{15}

_{2}) / (

^{16}

_{3}) = 0.1875).

*F*(3, 42) = 13.88,

*p*< 10

^{−5}). Trials in which subjects responded incorrectly were discarded.

*F*(1, 14) = 74.06,

*p*< 10

^{−6}for [Circle/Square],

*F*(1, 14) = 59.65,

*p*< 10

^{−5}for [Target/Distractor], with a significant interaction

*F*(1, 14) = 34.04,

*p*< 10

^{−4}showing that the effect is more pronounced for targets than for distractors). This bottom-up advantage for squares could have lead to spurious conclusions regarding the distribution of attention on trials in which the target shapes were different. We therefore only considered trials in which the target shapes were identical for subsequent analysis: that way, both target locations were expected to receive comparable amounts of exogenous attention.

*F*(1, 14) = 74.36,

*p*< 10

^{−6}for [target/distractor] and

*F*(3, 42) = 7.16,

*p*< 10

^{−3}for [SOA], with a significant interaction

*F*(3, 42) = 8.31,

*p*< 10

^{−3}). Letters at distractor locations were reported significantly less often than they would have been by chance (2-way ANOVA,

*F*(1, 14) = 7.57,

*p*< 0.05 for [distractor/chance] and

*F*(3, 42) = 0.44,

*p*= 0.73 for [SOA], with a significant interaction

*F*(3, 42) = 3.37,

*p*< 0.05). This is due to the manner chance is calculated, depending on the average number of letters reported by each subject, and it shows that the primary task was effective in making subjects attend selectively and almost exclusively to the target locations. Distractor locations that were between target locations did not receive more attention than other distractor locations at any SOA (2-way ANOVA,

*F*(1,14) = 2.85,

*p*= 0.11 for [between/outside] and

*F*(3, 42) = 0.46,

*p*= 0.71 for [SOA], with no significant interaction

*F*(3, 42) = 0.69,

*p*= 0.57), thus arguing against the possibility of a single extended spotlight encompassing both target locations. In Figure 4, probabilities of letter report conditional on the report of one target are plotted. The conditional probability of reporting the other target was significantly higher than the conditional probability of reporting a distractor, and this difference significantly increased with SOA, which reflects the previous observation that target letter report performance increases with SOA (see Figure 3; 3-way ANOVA,

*F*(1, 14) = 22.99,

*p*< 10

^{−3}for [target/distractor],

*F*(3, 42) = 4.12,

*p*< 0.05 for [SOA], and

*F*(3, 42) = 3.46,

*p*= <0.05 for [target separation], with a significant interaction between [target/distractor] and [SOA]

*F*(3, 42) = 4.63,

*p*< 0.01). Likewise, in the cases of one or two intervening distractors, the conditional probability of report for distractors between targets is not significantly different from the conditional probability of report for distractors outside targets at any SOA or any target separation (3-way ANOVA,

*F*(1, 14) = 0.752,

*p*= 0.40 for [distractor between/distractor outside],

*F*(3, 42) = 0.57,

*p*= 0.64 for [SOA], and

*F*(1, 14) = 1.98,

*p*= 0.18 for [target separation], with no significant interactions). At first sight, our data are thus compatible with the data that Bichot et al. (1999) based their conclusions on.

*F*(3, 42) = 9.50,

*p*< 10

^{−4}for [SOA],

*F*(1, 14) = 50.181,

*p*< 10

^{−5}for [T1/T2] with a significant interaction

*F*(3, 42) = 3.95,

*p*< 0.05). This result goes together with a significant effect of SOA on the discriminant (1-way ANOVA,

*F*(3, 42) = 3.25,

*p*< 0.05). A post-hoc analysis using Tukey's Honestly Significant Differences test shows that the discriminant at the longest SOA (213.3 ms) is significantly higher than at the shortest SOAs (53.3 ms and 106.6 ms). We can already conclude that the bias of attention for one target location over the other increases with time. Further tests show that for SOAs at or below 106.6 ms, the two target locations apparently received comparable amounts of attention: the discriminants across subjects did not statistically differ from zero (one sided

*t*-test,

*t*(14) = 1.27,

*p*= 0.11 at 53.3 ms and

*t*(14) = 0.93,

*p*= 0.18 at 106.6 ms); the discriminant estimated from the pooled data was close to zero (−0.01 at 53.3 ms and −0.01 at 106.6 ms), providing graphical confirmation. Note that this result is consistent with the conclusions of Bichot et al. (1999), who investigated a single SOA of 105 ms. For SOAs of 160 ms or greater, one of the target locations was found to win the attentional competition, receiving more attention as the SOA increased: the discriminants across subjects were statistically larger than zero (one sided

*t*-test,

*t*(14) = 3.54,

*p*< 0.01 at 160 ms and

*t*(14) = 3.36,

*p*< 0.01 at 213.3 ms) and the discriminant estimated from the pooled data was larger than zero (0.01 at 160 ms and 0.04 at 213.3 ms). These results are summarized in Figure 5.

*planning*a saccade. Indeed, our results are a natural prediction of a certain class of computational models of attention (Hamker, 2004) in which the planning of saccadic eye movements guides attentional selection, in line with the premotor theory of attention (Rizzolatti, Riggio, Dascola, & Umiltá, 1987). In this model of saccadic decision making and attention, the frontoparietal network receives the current output of a “refined” distributed saliency map (Hamker, 2006) and selects the unique location of an eye movement by a competition over time. Activity from this frontoparietal network is fed back continuously to extrastriate visual areas. Thus, the SOA determines the state of this competition at the time the letters are flashed, and ultimately the distribution of attention at different locations. While the amount of motor in the premotor theory has been a subject of intense debate (Chambers & Mattingley, 2005; Hamker, 2005; Juan etal., 2008; Juan, Shorter-Jacobi, & Schall, 2004; Thompson, Biscoe, & Sato, 2005) our results argue for feedback signals from cells in oculomotor areas that have knowledge about the motor plan.

*Journal of Vision, 2*(7):7, 7a, http://journalofvision.org/2/7/7/). This work was supported by the German Science Foundation (DFG HA2630/2-1) and the Federal Ministry of Education and Research Grant (BMBF 01GW0653), the CNRS (Grant CNRS-USA), the ANR (06JCJC-0154), the Fyssen Foundation, and the European Science Foundation (EURYI). We wish to acknowledge Kyle Cave and an anonymous referee for helpful advice and suggestions and Christof Koch for his continued support.