Supplementary data analyses
It is possible that the interaction effects we observed in all three experiments arise from strategic
reading or certain expectations built-up along the experiment. If this is true, trial should affect
the observed interaction effects. Our original model, however, does not include the variable trial
as part of the regression equation. Following the suggestions of the reviewers, we conducted
further analyses for those regions and measures in which we found reliable interaction effects
between card distance and semantic similarity. In these analyses we controlled for the effect of
trials by including the trial number as a control variable in the model (see, for instance,
Kuperman, V., Bertram, R., & Baayen, R. H. (2010). Processing trade-offs in the reading of
Dutch derived words. Journal of Memory and Language, 62, 83–97.), and furthermore we
conducted non-parametric correlation analyses between trial numbers and the dependent variable
by region and condition.
These analyses are aimed to examine the potential effects of trial on the observed interaction
effects. Including trial as control variable in our regression model subtracts the trial variance
from the variance due to the fixed factors and the interaction between them. Thus, if these
interaction effects come from variance that accumulates across the trials, including trial as a
control variable in the regression equation should decrease or eliminate the significance of the
interaction effects. Alternatively, if interaction effects are independent from the variance due to
the trials, significant interaction effects should remain significant even after the inclusion of trial
in the model.
The original model appears in (1), while the new model is presented in (2). In both models, “dv”
is the dependent variable (e.g., first-pass time), and “iv1” and “iv2” are the two independent
variables (i.e., spatial distance and semantic similarity). The new model includes the term “trial”
into the equation as a control variable. A summary of the results of the new regression model (2)
is presented in Table 1.
(1) lmer (dv ~ iv1*iv2
+ (1 + iv1*iv2 | participant)
+ (1 + iv1*iv2 | item), data)
(2) lmer(dv~(trial)+ iv1*iv2
+ (1+(trial)+iv1*iv2|participant)
+ (1+(trial)+iv1*iv2|item), data)
Table 1. Main and interaction effects (by experiment, region and measure) in the linear mixedeffect regression on log-transformed reading times for those regions in which initial analyses
revealed interaction effects.
Experiment
Experiment 1
Region
ADJ
VP2
NP3
NP3
Experiment 2
ADJ
ADJ
Experiment 3
NP2
Measure
First-pass
First-pass
First-pass
Total times
Regression path
Total times
First-pass
Fixed Effects
(Intercept)
Trial
Distance
Similarity
SxD
(Intercept)
Trial
Distance
Similarity
SxD
(Intercept)
Trial
Distance
Similarity
SxD
(Intercept)
Trial
Distance
Similarity
SxD
(Intercept)
Trial
Distance
Similarity
SxD
(Intercept)
Trial
Distance
Similarity
SxD
(Intercept)
Trial
Distance
Similarity
SxD
Estimate
5,678
-0,001
0,011
0,047
-0,021
5,307
-0,036
-0,010
0,021
-0,029
5,616
-0,081
-0,035
0,008
-0,040
5,774
-0,124
-0,024
0,017
-0,037
5,887
-0,066
-0,004
0,033
-0,025
5,893
-0,081
-0,008
0,024
-0,033
5,630
0,028
-0,018
0,037
-0,032
SE
0,032
0,013
0,013
0,018
0,011
0,030
0,016
0,015
0,012
0,013
0,050
0,024
0,020
0,016
0,018
0,055
0,027
0,017
0,021
0,018
0,035
0,015
0,012
0,017
0,014
0,038
0,018
0,012
0,018
0,014
0,050
0,014
0,015
0,018
0,014
t
178,22
-0,08
0,88
2,62
-1,95
176,04
-2,28
-0,68
1,69
-2,15
113,20
-3,44
-1,71
0,51
-2,18
104,99
-4,68
-1,40
0,80
-2,05
170,19
-4,26
-0,32
2,00
-1,76
153,82
-4,61
-0,65
1,34
-2,39
111,51
1,97
-1,21
2,03
-2,38
*
#
*
*
*
#
*
*
*
*
*
#
*
*
#
*
VP2
First-pass
(Intercept)
Trial
Distance
Similarity
SxD
5,380
-0,008
-0,005
0,000
-0,025
0,034
0,015
0,016
0,012
0,012
160,05
-0,56
-0,30
-0,01
-2,08
*
Note: #p <.1. *p <.05.
Table 1 reveals that the inclusion of trial in the regression model does not cause any large
differences (compared to the original model, see Tables 3, 5, and 7 in the article) in the observed
interactions. One of the reported significant interaction effects turned marginally significant
(Experiment 1, ADJ region, First-pass; t-value = -1.95). Nevertheless, all other effects that we
reported as significant remained statistically significant, and some t-values even increased after
controlling for trial effects.
Nonetheless, two potentially interesting results are observed with the new model. On the one
hand, the previously observed pervasive effect of similarity (semantically similar vs. dissimilar
content) was eliminated, suggesting it might have emerged over the course of the experiment.
Yet, the interaction effects remained while the main effect of similarity disappeared. This
supports the view that interaction effects between spatial distance and similarity are independent
from a potential learning effect, while the main effect of similarity is not. On the other hand,
most of the analyses revealed a significant main effect of trial. Thus, we conducted a series of
correlation analyses to further understand how trial affected the reading times measures. In
Table 2 we summarized the results of the non-parametric correlation between reading times and
trials by region and condition.
Table 2. Correlations between trials and reading times (by experiment, region, measure, and
condition) for those regions in which initial analyses revealed interaction effects.
Experiment
Experiment 1
Region
ADJ
Measure
First-pass
DISTANCE
close
far
VP2
First-pass
close
far
NP3
First-pass
close
far
NP3
Total times
close
far
Experiment 2
ADJ
Regression path
close
far
ADJ
Total times
close
far
Experiment 3
NP2
First-pass
close
far
VP2
First-pass
close
far
SIMILARITY
similar
dissimilar
similar
dissimilar
similar
dissimilar
similar
dissimilar
similar
dissimilar
similar
dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Similar
Dissimilar
Spearman’s rho
-0.019
-0.102
0.004
0.014
-0.084
-0.042
-0.124
-0.104
-0.043
0.008
-.238**
-.136*
-0.043
-0.106
-.301**
-.214**
-0.098
-0.097
-.165**
-.157**
-.188**
-0.110
-.167**
-.167**
0.115
-0.057
0.072
0.086
-0.033
-0.020
-0.039
-0.022
Sig. (2-tailed)
0.743
0.081
0.941
0.807
0.202
0.521
0.054
0.097
0.510
0.904
0.000
0.036
0.515
0.116
0.000
0.001
0.096
0.095
0.004
0.005
0.001
0.057
0.004
0.003
0.066
0.339
0.240
0.151
0.611
0.769
0.567
0.728
Note: *p <.05, **p <.01, ***p <.001
The results of the correlation analyses evidenced that whenever trial and reading times correlated
significantly, correlation were negative independently of the experimental conditions. These
findings suggest that the main effects observed in the linear mixed effects regressions translate in
a growing advantage on the reading times over the course of each experiment. After we
controlled for that advantage, previously observed interaction effects remained significant (see
Table 1). This suggests that trial effects cannot explain the interaction between spatial distance
and semantic similarity, since trial acted upon all conditions in the same manner.