**Research has shown that participants can extract the average facial expression from a set of faces when these were presented at fixation. In this study, we investigated whether this performance would be modulated by eccentricity given that neural resources are limited outside the foveal region. We also examined whether or not there would be compulsory averaging in the parafovea as has been previously reported for the orientation of Gabor patches by Parkes, Lund, Angelucci, Solomon, and Morgan (2001). Participants were presented with expressive faces (alone or in sets of nine, at fixation or at 3° to the left or right) and were asked to identify the expression of the central target face or to estimate the average expression of the set. Our results revealed that, although participants were able to extract average facial expressions in central and parafoveal conditions, their performance was superior in the parafovea, suggesting facilitated averaging outside the fovea by peripheral mechanisms. Furthermore, regardless of whether the task was to judge the expression of the central target or set average, participants had a tendency to identify central targets' expressions in the fovea but were compelled to average in the parafovea, a finding consistent with compulsory averaging. The data also supported averaging over substitution models of crowding. We conclude that the ability to extract average expressions in sets of faces and identify single targets' facial expressions is influenced by eccentricity.**

- A central model that predicts responses based on the central target alone.
- An average model that is associated with the aforementioned averaging of signals and that predicts responses based on the set average.
- A substitution model that is associated with spatial uncertainty and target–flanker swap and that predicts responses based on the flankers' properties.

*M*= 23.5 years,

*SD*= 6.91). Informed consent was obtained for all participants, and all had normal or corrected-to-normal vision. This study was approved by the research ethics committee at the University of Hull.

*° in eccentricity occurs when flankers are located within*

**φ***/2° of the targets. Although the faces are located 2.30° center to center (beyond 1.5° if*

**φ***= 3), they are nonetheless within 0.4° of each other side to side and 1.21° from center to side of the next horizontal face. All 11 variants of expressions were presented as central targets in the flanker-absent condition and as central targets and/or flankers in the flanker-present conditions. The example in Figure 2 shows an 80% disgusted central face surrounded by eight identical 80% happy flanker faces.*

**φ***i*refers to the trial number and

*n*is the total number of responses. Lower MSE values, smaller error, correspond to stronger performances. We selected MSE values to describe participants' performance because our aim was to identify how much participants' responses deviated away from actual expressions and not how these could be biased toward happy or disgusted faces.

*i*refers to the trial number and

*n*is the total number of responses. Stronger model performances are reflected by lower MSE values.

*F*(1, 17) = 38.58,

*p*< 0.001,

*η*= 0.69. When asked to identify the central targets' expressions, participants were more accurate when target faces were presented alone (

^{2}*MSE*= 7.24,

*SD*= 0.37) compared to when they were presented among flankers (

*MSE*= 10.62,

*SD*= 0.52).

*F*(2, 34) = 34.05,

*p*< 0.001,

*η*= 0.67. Responses were more accurate in the foveal condition (

^{2}*MSE*= 6.15,

*SD*= 0.43) compared to parafoveal, left vs. right (

*MSE*= 10.42,

*SD*= 0.55 and

*MSE*= 10.20,

*SD*= 0.50, respectively). Bonferroni post hoc tests revealed significant differences between foveal and left (

*d*= 0.93) and foveal and right (

*d*= 0.74) but none between left and right (

*d*= 0.06).

*F*(2, 34) = 23.67,

*p*< 0.001,

*η*= 0.58. To determine the cause(s) of this interaction, we examined two sets of simple main effects. First, we compared the effect of flankers at each eccentricity. In foveal vision, participants' performances were similar in the flanker-present and -absent conditions,

^{2}*F*(1, 17) = 3.84,

*p*> 0.05 (

*MSE*= 6.88,

*SD*= 0.41 and

*MSE*= 5.44,

*SD*= 0.68, respectively). However, in the parafovea, flankers had a detrimental effect on overall performance: Errors were significantly higher in the flanker-present condition compared to the flanker-absent condition:

*F*(1, 17) = 32.78,

*p*< 0.01,

*η*= 0.66 and

^{2}*F*(1, 17) = 40.15,

*p*< 0.01,

*η*= 0.70 for left and right, respectively. At left and right, the data points along the solid line (flanker present) are higher compared to the points on the dashed line (flanker absent); Cohen's

^{2}*d*values for left and right conditions were 1.35 and 1.50, respectively.

*F*(2, 34) = 2.75,

*p*= 0.08,

*η*= 0.21. When participants were asked to identify the central targets' expressions among flankers (solid black line in Figure 6), there was a significant effect of eccentricity,

^{2}*F*(2, 34) = 30.52,

*p*< 0.001,

*η*= 0.64. Bonferroni post hoc analyses revealed that performance was better in the fovea (

^{2}*MSE*= 5.44,

*SD*= 0.68) compared to the left (

*MSE*= 13.27,

*SD*= 0.97,

*d*= 2.04) and right (

*MSE*= 13.14,

*SD*= 0.85,

*d*= 1.36). There was no difference between the left and right conditions (

*d*= 0.02). This indicates that both factors flanker and eccentricity affected each other.

*F*(1, 17) = 12.53,

*p*< 0.005,

*η*= 0.42, where participants were more accurate on the average condition (

^{2}*MSE*= 8.24,

*SD*= 0.41) compared to the central condition (

*MSE*= 10.62,

*SD*= 0.52). There was a significant effect of eccentricity,

*F*(2, 34) = 14.73,

*p*< 0.001,

*η*= 0.46: Participants' performance was superior in foveal vision (

^{2}*MSE*= 7.99,

*SD*= 0.40) compared to left and right (

*MSE*= 10.22,

*SD*= 0.44 and

*MSE*=10.07,

*SD*= 0.43, respectively;

*d*= 0.33 and 0.27, respectively). There were no significant differences between the two parafoveal conditions (

*d*= 0.04).

*F*(2, 34) = 31.38,

*p*< 0.001,

*η*= 0.65. To determine the cause(s) of this interaction, we examined two sets of simple main effects. First, we compared the effect of task at each eccentricity. When faces were presented in the fovea, participants were better at rating the central expression (

^{2}*MSE*= 5.44,

*SD*= 0.68) compared to estimating the average of the sets of faces (

*MSE*= 10.54,

*SD*= 0.70),

*F*(1, 17) = 20.81,

*p*< 0.001,

*η*= 0.55. When faces were presented in the parafovea, participants were poorer at rating the central expression (

^{2}*MSE*= 13.27,

*SD*= 0.70 and

*MSE*= 13.12,

*SD*= 0.85 for left and right, respectively) compared to estimating the average of the sets of faces (

*MSE*= 7.18,

*SD*= 0.57 and

*MSE*= 7.01,

*SD*= 0.37 for left and right, respectively),

*F*(1, 17) = 21.01,

*p*< 0.001,

*η*= 0.55 and

^{2}*F*(1, 17) = 37.48,

*p*< 0.001,

*η*= 0.67 for left and right.

^{2}*MSE*= 5.44,

*SD*= 0.68) compared to left and right (

*MSE*= 13.27,

*SD*= 0.97 and

*MSE*= 13.14,

*SD*= 0.85, respectively),

*F*(2, 34) = 30.52,

*p*< 0.001,

*η*= 0.64. When participants were asked to estimate the average expression of a group of faces (red line in Figure 5), their performance was significantly better in the left and right (

^{2}*MSE*= 7.18,

*SD*= 0.57 and

*MSE*= 7.01,

*SD*= 0.37, respectively) compared to the fovea (

*MSE*= 10.54,

*SD*= 0.70),

*F*(2, 34) = 18.04,

*p*< 0.001,

*η*= 0.52. This indicates that both factors task and eccentricity affect each other.

^{2}*F*(4, 68) = 31.30,

*p*< 0.001,

*η*= 0.65. First, we compared the effect of model at each eccentricity. In the fovea, there was a significant effect of model,

^{2}*F*(2, 34) = 47.55,

*p*< 0.001,

*η*= 0.74. Bonferroni post hoc tests revealed that the central model was the most accurate in predicting participants' responses (

^{2}*MSE*= 5.44,

*SD*= 0.68) and was superior to the average and substitution models (

*MSE*= 12.25,

*SD*= 0.75 and

*MSE*= 15.33,

*SD*= 0.88,

*d*= 1.33 and 1.72, respectively). The average model, in turn, was significantly better than the substitution model (

*d*= 4.73). In the parafovea, model also had a significant effect,

*F*(2, 34) = 5.84,

*p*= 0.007,

*η*= 0.26 and

^{2}*F*(2, 34) = 15.49,

*p*< 0.001,

*η*= 0.48, for left and right, respectively. In the left, the average model (

^{2}*MSE*= 9.12,

*SD*= 0.68) was superior to both the central and substitution models (

*MSE*= 13.27,

*SD*= 0.97 and

*MSE*= 10.83,

*SD*= 0.82, respectively;

*d*= 0.68 for average vs. central, and 2.23 for average vs. substitution), and there were no differences between the central and substitution models (

*d*= 0.66). However in the right, the average model (

*MSE*= 8.10,

*SD*= 0.43) was superior to both the central and substitution models (

*MSE*= 13.14,

*SD*= 0.85 and

*MSE*= 9.69,

*SD*= 0.52, respectively;

*d*= 1.09 for average vs. central, and 2.74 for average vs. substitution), and the substitution model was better than the central model (

*d*= 0.66).

*F*(2, 34) = 30.52,

*p*< 0.001,

*η*= 0.64: Performance was significantly stronger in the fovea (

^{2}*MSE*= 5.44,

*SD*= 0.68) compared to the left and right conditions (

*MSE*= 13.27,

*SD*= 0.97 and

*MSE*= 13.14,

*SD*= 0.85, respectively;

*d*= 2.04 and 1.36, respectively). Results of the left and right conditions were comparable (

*d*= 0.02). For the average model (in green in Figure 6A), there was a significant effect of eccentricity,

*F*(2, 34) = 21.60,

*p*< 0.001,

*η*= 0.56: Performance was significantly weaker in the fovea (

^{2}*MSE*= 12.25,

*SD*= 0.75) compared to the left and right conditions (

*MSE*= 9.12,

*SD*= 0.68 and

*MSE*= 8.10,

*SD*= 0.43,

*d*= 1.33 and 1.30, respectively). No difference was found between left versus right (

*d*= 0.36). For the substitution model (in yellow in Figure 6A), there was a significant effect of eccentricity,

*F*(2, 34) = 24.86,

*p*< 0.001,

*η*= 0.59: As was in the case of the average model, performance was significantly weaker in the fovea (

^{2}*MSE*= 15.23,

*SD*= 0.86) compared to the left and right conditions (

*MSE*= 10.83,

*SD*= 0.82 and

*MSE*= 9.69,

*SD*= 0.52,

*d*= 1.49 and 1.37, respectively). No difference was found between results of left versus right,

*d*= 0.30.

*F*(4, 68) = 26.37,

*p*< 0.001,

*η*= 0.61. The data is presented in Figure 6B. First, we compared the effect of model at each eccentricity. In the fovea, there was a significant effect of model,

^{2}*F*(2, 34) = 17.73,

*p*< 0.001,

*η*= 0.74. Bonferroni post hoc tests revealed that the central model was the most accurate in predicting participants' responses (

^{2}*MSE*= 7.35,

*SD*= 0.62) and was superior to the average and substitution models (

*MSE*= 10.54,

*SD*= 0.70 and

*MSE*= 13.17,

*SD*= 0.82,

*d*= 0.66 and 1.06, respectively). The average model, in turn, was significantly better than the substitution model (

*d*= 4.26). In the parafovea, model also had a significant effect,

*F*(2, 34) = 15.45,

*p*< 0.001,

*η*= 0.48 and

^{2}*F*(2, 34) = 32.54,

*p*< 0.001,

*η*= 0.66 for left and right, respectively. In the left, the average model (

^{2}*MSE*= 7.18,

*SD*= 0.57) was superior to both the central and substitution models (

*MSE*= 13.97,

*SD*= 1.08 and

*MSE*= 8.55,

*SD*= 0.73,

*d*= 1.06 and 1.67, respectively), and the substitution model was better than the central model (

*d*= 0.75). Likewise, in the right, the average model (

*MSE*= 7.01,

*SD*= 0.37) was superior to both the central and substitution models (

*MSE*= 14.11,

*SD*= 0.94 and

*MSE*= 8.34,

*SD*= 0.45,

*d*= 1.77 and 2.25, respectively), and the substitution model was again better than the central model (

*d*= 1.56).

*F*(2, 34) = 27.91,

*p*< 0.001,

*η*= 0.62: Performance was significantly stronger in the fovea (

^{2}*MSE*= 7.35,

*SD*= 0.62) compared to the left and right conditions (

*MSE*= 13.97,

*SD*= 1.08 and

*MSE*= 14.11,

*SD*= 0.94,

*d*= 1.59 and 1.31, respectively). Results for the left versus right were comparable (

*d*= 0.04). For the average model (in green in Figure 6B), there was a significant effect of eccentricity,

*F*(2, 34) = 18.04,

*p*< 0.001,

*η*= 0.52: Performance was significantly weaker in the fovea (

^{2}*MSE*= 10.54,

*SD*= 0.70) compared to the left and right conditions (

*MSE*= 7.18,

*SD*= 0.57 and

*MSE*= 7.01,

*SD*= 0.37,

*d*= 1.01 and 1.15, respectively). Results for left versus right were similar (

*d*= 0.09). For the substitution model (in yellow in Figure 6B), there was a significant effect of eccentricity,

*F*(2, 34) = 20.41,

*p*< 0.001,

*η*= 0.55: As was in the case of the average model, performance was significantly weaker in the fovea (

^{2}*MSE*= 13.17,

*SD*= 0.82) compared to the left and right conditions (

*MSE*= 8.55,

*SD*= 0.73 and

*MSE*= 8.34,

*SD*= 0.45,

*d*= 1.08 and 1.18, respectively), no difference was found between results of left versus right (

*d*= 0.09).

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