Supplementary Material

Method

Stimulus Selection

We selected the most typical female Asian and Caucasian faces as the face stimuli by randomly

sampling 19 participants from the same population who did not join the classification experiments to

complete a rating study. Participants rated 45 female Asian faces and 45 female Caucasian faces about

their typicality (“How typical the female Asian/Caucasian face do you feel?”) using a 5-point Likert

scale (1 for the least typical to 5 for the most typical). The mean score for the most typical female

Asian face was 4.16 and the mean score for the most typical female Caucasian face was 4.00.

We used Photoshop to design the face stimuli which allows the distance between facial features

to be changed. Following SFT, we adopted the double factorial paradigm such that the distance

between eyes and the distance between nose and mouth were manipulated into three levels,

respectively. See Figure 1, the values of e1, e2, and e3 on the x-axis (eye-to-eye separation)

correspond to a distance of 37 pixels, 46 pixels, and 52 pixels between eye centers. Values of n1, n2,

and n3 on the y-axis (nose-to-mouth separation) corresponded on a distance of 9 pixels, 14 pixels, and

17 pixels between the nose base and the upper lip. The size of a face was 167 to 236 pixels which

subtended a visual angle of about 2.4° to 3.5°.

Tests of Effective Selective Influence

Two levels of analyses were conducted. First, mean RTs (for Category A) were analyzed with a

2 (saliency of eye separation) x 2 (saliency of lip position) ANOVA. If the selective-influence

assumptions are satisfied, we expect to observe significant main effects of the two salience

manipulations. Second, the RT distributions were examined. If this assumption is satisfied, we expect

to observe that the marginal distribution of the HH+HL conditions is significantly different from that

of the LH+LL conditions suggesting that the salience manipulation on eye separation is effective and

that the marginal distribution of the HH+LH conditions is significantly different from that of the

HL+LL conditions suggesting that the salience manipulation on lip position is effective. We

additionally applied a number of Komolgorov-Smirnoff (K-S) tests testing the relationship between

the distributions (e.g,. that SHH(t) < {SLH(t), SHL(t)} < SLL(t)). The qualitative results of these tests are

shown in Table S1.

Table S1. Results of K-S tests of stochastic dominance, along with significance tests of the maximum (D+) and minimum (D-) deflection and an adjusted rank transform test of the MIC.

Subject Condition Stochastic Dominance D+ p D- p MIC pS1 1 HH == LH 0.09 0.15 0.03 0.84 59 0.007S2 1 ok 0.1 0.09 0.028 0.83 38 0.01S3 1 HH == LH, HL == LL 0.11 0.06 0.01 0.98 37 0.03S4 1 HH == LH 0.17 < .001 0.022 0.89 42.4 < .001S5 1 HH == LH, HL == LL 0.07 0.29 0.06 0.41 48.76 0.43S6 1 HH == LH 0.11 0.05 0.03 0.79 24.8 0.06S7 1 ok 0.15 0.005 0.04 0.71 27.12 0.001S8 1 HH == LH 0.095 0.12 0.03 0.84 20.94 0.11S9 1 ok 0.12 0.06 0.08 0.25 20.22 0.09

S10 1 ok 0.17 0.001 0.034 0.73 62.3 < .001S1 2 HH == LH 0.08 0.23 0.01 0.95 6.01 0.21S2 2 HH == LH, HL == LL 0.01 0.97 0.08 0.29 -11.8 0.07S3 2 HH == LH, HL == LL 0.04 0.68 0.07 0.36 2.02 0.79S4 2 HH == LH 0.07 0.36 0.05 0.51 -10.84 0.72S5 2 HH == LH, HL == LL 0.048 0.6 0.06 0.44 2.45 0.98S6 2 ok 0.08 0.22 0.07 0.36 12.58 0.32S7 2 ok 0.09 0.13 0.02 0.87 4.56 0.06S8 2 HH == LH, HL == LL 0.06 0.45 0.02 0.89 8.25 0.3S9 2 HH == LH, HL == LL 0.05 0.65 0.06 0.48 -1.05 0.41

S10 2 ok 0.17 0.001 0.038 0.71 71.66 < .001Note that Condition 1 denotes the own-race face condition and Condition 2 denotes the other-race

face condition.

Own-race faces. Figure S1 shows the plots of four survivor functions of Category A for each

participant. Based on the visual inspection, in most cases, the survivor functions gradually shifted

from the HH, HL, and LH conditions to the LL condition. We further used the Kolmogorov-Smirnov

(K-S) test to test the group-level results. Results showed that the marginal distribution of the HH+HL

condition was significantly different from that of the LH+LL condition (KS = 0.076, p < 0.001) and

the marginal distribution of HH+LH condition was significantly different from that of the HL+LL

condition (KS = 0.162, p < 0.001), suggesting that the salience manipulations were effective at the RT

distribution level. The results in Table S1 show that in some cases, the K-S test showed no significant

difference between the HH and LH condition. The implication is that for these participants, the RT

distributions for these two stimuli are collapsed. Likewise, for two additional subjects, the RT

distributions are also collapsed for the HL and LL stimuli. While not conclusive evidence for one

architecture over the other, the collapsed HH and LH (but not HL and LL) survivor functions are

consistent with the theory that processing occurred in parallel but that processing of lip position was

faster than for eye separation. When one dimension is much faster than the other, the statistical

minimum time benefits of parallel processing can be lost rendering the HH distribution equivalent to

the HL distribution. In two cases (S3 and S5), both the HH and LH distributions and the LH and LL

distributions are collapsed. As we argue in the main text and below, while not conclusive, this is

consistent with serial self-terminating processing.

Figure S1. Plots for the survivor functions of the four faces in Category A in the own-race

experiment.

Other-race faces. Figure S2 shows the plots of four survivor functions of Category A for each

participant. Based on the visual inspection, the four survivor functions were ordered. The survivor

functions gradually shifted from the HH, HL, and LH conditions to the LL condition. In addition, for

most participants, the survivor functions of the HH and LH conditions overlapped, while the survivor

functions of the LL and HL conditions overlapped. We further used the K-S test to test the group

results. Results showed that the marginal distribution of the HH+HL condition was significantly

different from that of the LH+LL condition (KS = 0.044, p < 0.001) and the marginal distribution of

HH+LH condition was significantly different from that of the HL+LL condition (KS = 0.145, p <

0.001), suggesting that the salience manipulations were effective at the RT distribution level. The

results in Table S1 show that for most subjects in this experiment, the K-S test showed no significant

difference between the HH and LH stimulus or between the HL and LL stimulus. As we argue in the

main text, this is good evidence that for these subjects, mouth position is being processed exclusively.

This is, thus, consistent with the assumption of serial self-terminating processing for these

participants.

Figure S2. Plots for the survivor functions of the four faces in Category A in the other-race

experiment.

Bootstrapped MIC results

Figure S3. Results of the MIC and the 95% CI for MIC for each participant and the entire

group in the own-race experiment.

Figure S4. Results of the MIC and the 95% CI for MIC for each participant and Group SS in the

other-race experiment.

Individual ANOVA results

Table S2. Results of two-way ANOVA on the mean RT of the four conditions of Category A for each

participant in the own-race experiment.

Eye separation Lip position

Eye separation

Lip position

F F F MSE dfe

S1 4.97* 51.88*** 4.34* 97493 1943

S2 25.93*** 143.20*** 9.33** 18947 1929

S3 1.76 73.63*** 4.01* 39245 1881

S4 7.00** 110.95*** 6.83** 30865 1876

S5 0.39 10.85** 3.77 (p = .052) 73994 1875

S6 14.19*** 87.61*** 9.41** 7822 1914

S7 33.93*** 92.34*** 13.94*** 6259 1903

S8 6.57* 36.47*** 2.96 (p = 0.08) 17568 1893

S9 33.20*** 38.23*** 3.51 (p = .06) 12272 1695

S10 144.58*** 91.81*** 22.92*** 20593 1943

Note: F represents the F statistics, and MSE represents the mean square error. The numerator

degree of freedom for all effects is 1. * p < .05. ** p < .01. *** p < .001.

Table S3. Results of two-way ANOVA on the mean RT of the four conditions of Category A for each

participant in the other-race experiment.

Eye separation Lip position

Eye separation

Lip position

F F F MSE dfe

S1 2.40 49.96*** 0.31 13610 1873

S2 0.03 111.35*** 3.16 4752 1737

S3 1.98 113.88*** 0.02 28011 1920

S4 0.32 199.39*** 0.54 25838 1883

S5 0.004 30.44*** 0.05 14348 1835

S6 7.65** 76.63*** 1.08 17406 1901

S7 3.94* 130.417*** 0.50 5068 1938

S8 2.44 24.84*** 0.43 15343 1529

S9 0.75 38.06*** 0.02 7406 1651

S10 151.13*** 60.16*** 33.65*** 18675 1955

Note: F represents the F statistics, and MSE represents the mean square error. The numerator

degree of freedom for all effects is 1. * p < .05. ** p < .01. *** p < .001.

Statistical SIC Tests

To test whether the SIC function was significantly different from zero we applied Houpt-

Townsend tests to the maximum positive (D+) and negative (D-) defections from 0 using the SFT [R]

toolbox (Houpt et al., 2014; see also Houpt & Townsend, 2010). Rather than using the conventional

alpha rate of .05, which biases a normal statistical test result toward the null to reduce Type I error,

Fox and Houpt (2016) recommend using an alpha rate of .33 since the “null” hypothesis of SIC = 0, in

this case, represents serial self-termination. The results of these tests were generally supportive of our

conclusions. For instance, the D+ statistic was significant (at p < .33) for all of the participants in the

own-race experiment while the D- statistic was not significant for any participant with exception of

S9. By contrast, in the other-race experiment, the D+ statistic was generally not significant with the

exception of S1, S6, S7, and S10. The D- statistic was also significant at the p < .33 level for S2.

Taken together with our other results, the SIC statistics support the conclusion that processing shifted

from parallel self-termination in the own-race experiment to serial self-termination in the other-race

experiment.

We also report an adjusted-rank transform test for the MIC value. In line with our ANOVA and

non-parametric bootstrapping results, this test was generally significant for participants in the own-

race experiment but not the other-race experiment (with the exception of S10).

Supplementary References

Fox, E. L., & Houpt, J. W. (2016). The perceptual processing of fused multi-spectral imagery.

Cognitive Research: Principles and Implications, 1, 31.

Houpt, J. W., Blaha, L. M., McIntire, J. P., Havig, P. R., & Townsend, J. T. (2014). Systems factorial

technology with R. Behavior Research Methods, 46, 307-330.

Houpt, J. W., & Townsend, J. T. (2010). The statistical properties of the survivor interaction contrast.

Journal of Mathematical Psychology, 54, 446-453.