The identification of a peripheral target surrounded by flankers is often harder than the identification of an identical isolated target. This study examined whether this crowding phenomenon, and particularly its spatial extent, is affected by the allocation of spatial attention to the target location. We measured orientation identification of a rotated T with and without flankers. The distance between the target and the flankers and their eccentricity varied systematically. We manipulated attention via peripheral precues: in the cued condition, a dot indicated the target location prior to its onset. On the neutral condition, a central disk conveyed no information regarding the target location (Experiments 1–2), and on the invalid condition (Experiment 3), an invalid cue attracted attention to a nontarget location. We found, across all experiments, at all eccentricities, a significant attentional enhancement of identification accuracy. Most importantly, we found a significant attentional reduction of the critical distance (i.e., the target–flankers distance at which the flankers no longer interfere with target identification). These attentional effects were found regardless of the presence or absence of a backward mask and whether the attentional cue was informative or not. These findings suggest that attention reduces the spatial extent of crowding.

^{2}) were presented on a darker background (17 cd/m

^{2}), resulting in a contrast of 10%, and both subtended 1.05° × 1.05° of visual angle. There were nine possible distances between the flankers and the target, varying randomly from 1 to 9 in units of target width (e.g., Scolari et al., 2007). On 10% of the trials, the target appeared without flankers to provide a baseline. Target and flankers appeared to the left or right of fixation. There were three possible eccentricity conditions: 3°, 5°, or 9°. The peripheral cue was a green dot with a diameter of 0.35°, positioned at a nearer eccentricity, 1° closer to fixation than the target. The peripheral cue always indicated the correct target location. The neutral cue was a green disk, with a diameter of 0.55°, presented at the center of the screen. The fixation mark was a black (0.3 cd/m

^{2}) cross (0.3° × 0.3°) presented at the center of the screen, and the mask was a 23.3° × 1.1° gray and white random dot rectangle.

*F*(1, 43) = 34.81,

*p*< 0.0001] showing higher accuracy for cued than neutral trials. The main effect of target eccentricity was also significant [

*F*(2, 43) = 6.1,

*p*< 0.005]—accuracy decreased as target eccentricity increased. As in many previous studies of crowding (e.g., Bouma, 1970; Felisberti et al., 2005; Pelli et al., 2004; Poder, 2007; Scolari et al., 2007; Strasburger, 2005; Strasburger, Harvey, & Rentschler, 1991), a significant main effect was found for target–flankers distance [

*F*(8, 344) = 653.43,

*p*< 0.0001] demonstrating increased accuracy with increased target–flankers distance. A significant interaction was found between eccentricity and target–flanker distance [

*F*(16, 27) = 3.65,

*p*< 0.0001; Figure 2a]. This interaction emerged because except for the smallest target–flankers distance, the difference between the different eccentricities was more pronounced for smaller distances. At the smallest target–flankers distance, there was no difference between the different eccentricities—performance was close to guessing level at all eccentricities. The interaction between cue type and target–flanker distance was also significant [

*F*(8, 344) = 4.41,

*p*< 0.0001; Figure 2b]. This interaction emerged because unlike the other distances, there was no effect of cue type with the smallest target–flankers distance. At this distance, performance was close to guessing level for both cue types. No other effect reached statistical significance.

*F*(1,43) = 4.92,

*p*< 0.05]: accuracy was higher in the cued than neutral condition. The two-way interaction was not significant indicating that this cueing effect did not vary significantly as a function of target eccentricity.

*pc*is proportion correct,

*a*is the asymptote,

*s*is the scaling factor,

*d*is the target–flanker distance, and

*i*is the

*x*-intercept. The asymptotic value, scaling factor, and

*x*-intercept were adjusted using nonlinear least-squares fitting method (with a Trust-Region algorithm provided in MATLAB Curve Fitting Toolbox). The critical distance

*c*was defined as the target–flanker distance at which accuracy achieved 90% of the asymptotic value, and it was calculated using the following equation:

*R*

^{2}= 0.95). Figure 3a demonstrates the outcomes of the fitting process of one exemplar participant. Two participants were removed from further analysis because their data did not reach asymptote level (i.e., the estimated critical distance was exceptionally large). A two-way mixed design ANOVA (within variable: cue type; between variable: eccentricity) was conducted on the critical distances calculated based on the individual data of each cueing condition at each eccentricity. As expected, this analysis revealed a significant effect of eccentricity [

*F*(2, 41) = 7,

*p*< 0.005]: The critical distance was larger as the target appeared at larger eccentricities. This finding suggests that the critical distance scales with target eccentricity and it was previously demonstrated by various studies (e.g., Bouma, 1970; Latham & Whitaker, 1996; Pelli et al., 2004; Strasburger, 2005; Toet & Levi, 1992). Most relevant for the goal of this study, the analysis also revealed a significant cueing effect [

*F*(1, 41) = 14.82,

*p*< 0.0005; Figure 4]: the critical distance for the cued condition was significantly smaller than for the neutral condition. There was no significant interaction between cue type and eccentricity [

*F*< 1]. Indeed, planned comparisons confirmed that this cueing effect was significant at all eccentricities [3°:

*t*(14) = 2.82,

*p*< 0.007; 5°:

*t*(13) = 2.52,

*p*< 0.02; 9°:

*t*(14) = 2.07,

*p*< 0.03].

*R*

^{2}= 0.97). We then submitted these new estimations of the critical distance to the same statistical analysis and found the same pattern of results: the main effects of eccentricity and cue type were significant [cue type:

*F*(1, 41) = 21.97,

*p*< 0.0001; eccentricity:

*F*(2, 41) = 4.7,

*p*< 0.02; Figure 4], but their interaction was not [

*F*< 1]. Planned comparisons confirmed again that the cueing effect was significant at all eccentricities [3°:

*t*(14) = 2.65,

*p*< 0.01; 5°:

*t*(13) = 3.6,

*p*< 0.002; 9°:

*t*(14) = 2.81,

*p*< 0.008]. Table 1 lists the averaged critical distance values that were estimated with both methods. We also compared the cueing effect on the critical distance with both methods of estimation and found that the effect did not vary significantly as a function of method [

*F*< 1]. Hence, the finding that attention can reduce the spatial extent of crowding does not depend on the method used to estimate this extent.

3° | 5° | 9° | ||||
---|---|---|---|---|---|---|

Exponential | Two lines | Exponential | Two lines | Exponential | Two lines | |

Cued | 2.85 (2.99°) | 2.71 (2.85°) | 3.15 (3.31°) | 3.24 (3.40°) | 4.13 (4.33°) | 3.70 (3.89°) |

Neutral | 3.49 (3.66°) | 3.26 (3.42°) | 3.61 (3.79°) | 3.64 (3.82°) | 4.95 (5.2°) | 4.45 (4.67°) |

In target width units | In degrees of visual angle | |
---|---|---|

Experiments 1 and 3 | Experiment 2 | |

1 | 1.05 | 0.9 |

2 | 2.1 | 1.8 |

3 | 3.2 | 2.7 |

4 | 4.2 | 3.6 |

5 | 5.3 | 4.5 |

6 | 6.3 | 5.4 |

7 | 7.4 | 6.3 |

8 | 8.4 | 7.2 |

9 | 9.5 | 8.1 |

10 | – | 9 |

11 | – | 9.9 |

12 | – | 10.8 |

*F*(1, 14) = 7.04,

*p*< 0.02] and accuracy increased with increasing target–flankers distance [

*F*(11, 154) = 146.46,

*p*< 0.0001]. The interaction was also significant [

*F*(11, 154) = 3.38,

*p*< 0.0005] due to the fact that the cueing effect was mainly present for the smaller target–flankers distances (Figure 5). Finally, there was no significant difference between averaged accuracy in the two cueing conditions of the trials with no flankers [

*F*< 1].

*R*

^{2}= 0.92). Three participants were removed from further analysis because their data did not reach asymptote level. A one-way repeated measures ANOVA revealed a significant effect of cueing: [

*F*(1, 11) = 18.88,

*p*< 0.002; Figure 6]: the critical distance for the cued condition was significantly smaller than for the neutral condition (see the averaged critical distance values in Table 3), indicating a smaller critical distance when the target location was cued. A similar significant cueing effect on the critical distance emerged [

*F*(1, 11) = 6.85,

*p*< 0.03] when the critical distance was estimated for each participant using the two-lines method described above (mean

*R*

^{2}= 0.96), and as in Experiment 1, this effect did not significantly interacted with the factor of estimation method [

*p*= 0.16].

Experiment 2 | Experiment 3 | |||
---|---|---|---|---|

Exponential | Two lines | Exponential | Two lines | |

Cued | 3.52 (3.17°) | 3.39 (3.05°) | 3.80 (3.99°) | 3.32 (3.49°) |

Neutral (Experiment 2)/invalid (Experiment 3) | 4.38 (3.94°) | 4.08 (3.67°) | 4.63 (4.86°) | 4.15 (4.36°) |

*p*< 0.001 for both estimation methods). This result replicates Vickery, Shim, Chakravarthi, Jiang, and Luedeman's (2009) finding that when the target is masked by a backward mask crowding occurs far beyond the typical critical distance. They suggested that this finding reflects strong interactions between masking and crowding, which implies nonadditive relationships.

*valid*trials—the attentional cue appeared next to the target location, and on the other half—the

*invalid*trials—it appeared next to the other location. Thus, the attentional cue in this experiment is no longer informative, and the observers have no incentive to voluntarily attend the cued location. If transient attention can alleviate crowding effects, even when no voluntary mechanisms are involved, the attentional reduction of the critical distance in the valid trials should resemble those of the previous experiments of this study.

*F*(1, 15) = 12.29,

*p*< 0.004] and increasing target–flankers distance increased accuracy [

*F*(8, 120) = 341.34,

*p*< 0.0001]. The cue validity × target–flanker distance interaction was also significant [

*F*(8, 120) = 4.64,

*p*< 0.0001; Figure 7]; the cueing effect was largest at the smaller target–flankers distances, though not at the smallest distance at which performance was close to guessing level.

*F*(1, 15) = 3.01,

*p*= 0.1033].

*R*

^{2}= 0. 95; two lines: mean

*R*

^{2}= 0.97). One participant was removed from further analysis because her data did not reach asymptote level. The averaged critical distance values are listed in Table 3. We performed the same statistical analysis as in Experiment 2 on both estimations of the critical distance and found similar outcomes: the critical distance was smaller when a valid cue attracted attention to the target location than when an invalid cue attracted attention away from the target [exponential:

*F*(1,14) = 19.98,

*p*< 0.0005; two lines:

*F*(1,14) = 14.27,

*p*< 0.002; Figure 8]. Here too, this cueing effect did not interact significantly with the method of estimation [

*F*< 1]. The fact that precueing the target location decreased the critical distance when the peripheral cue was not informative suggests that transient attention can diminish crowding effects even without voluntary allocation of attention.