Supplementary material
S1: Individual relation to egocentric ratio in both experiments.
We observed a significant effect of egocentric ratio on participants’ PSE results (see results
section of experiment 2). Specifically, as the rooms became narrower and deeper across the
egocentric width:depth ratios 3:1, 2:1, 1:1, 1:2, 1:3, coded as r = 0, 1, 2, 3, 4, the mean PSE
decreased. To learn more about individual variations in responses, we plotted the slope from
each participant individually, i.e. their egocentric ratio coefficient, b1, in the regression
y = b0 + b1 r (Fig. S1). The mean slope across egocentric ratio was -6.54, with SD=14.94 due to
individual variation. A high variation would mean that the overall slope was not significantly
different from zero, i.e. it would produce a t-value closer to zero. A t-test showed the overall
slope was significantly different from zero [ t(67) = -3.61, p < .001]. This can be seen by the
leftward shift of the distribution in Fig. S1. The same was also the case for the coefficients from
experiments separately: for the laptop display type [t(35) = -2.79, p = .0085] and for the headmounted display type [t(31) = -2.27, p = .031]. In summary, individual variation was present as
expected, and was small enough to detect a significant decreasing slope across egocentric ratios
in each experiment.
Fig. S1. Frequency plot of egocentric ratio coefficients, or slopes, from each subject separately in both experiments.
The slope shows how much a participant’s PSE changes across egocentric ratio as rooms get narrower and deeper. A
slope of zero would mean that the participants’ PSEs were approximately equal for all room ratios. The frequency
distribution has a leftward shift away from zero, which is significant (p < .001, see text), indicating the general
tendency for PSEs to reduce across egocentric ratios.
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S2: Visual comparison of model fits
Fig. S2. The PSE difference as per Fig. 3, shown for a larger range of width:depth ratios, with the predictions for
experiment 1 from the power law model (solid line, equation 2) and the model of linear bias of egocentric ratio
(dashed line, equation 4). Error bars represent ± 1 std. error. Stimuli that fall exactly on the predictions for a model
(solid line or dashed line) would be predicted to be perceived as equal in volume to the constant stimulus according
to that model. Any stimuli above the model predictions (solid line or dashed line) would be perceived as larger than
the constant stimulus according that model, and below the lines as smaller. As a specific example, consider a room
of 1m width and 11m depth, which is 60m3 smaller than the constant stimulus. The value -60m3 lies above the
dashed line at the 1:11 ratio, and so this room would be predicted as being judged as larger than the constant
stimulus, i.e. the predicted probability participants would respond larger is greater than 0.5 according to the model of
linear bias. As a comparison, the same room of 1m by 11m lies below the solid line, and would be predicted as
“smaller” by the power law model. In summary, while both models are a good fit to our data (see section “A linear
bias based on egocentric ratio” for more details), the power law model gives more conservative predictions
compared to the model of linear bias in the case of more elongated rooms.
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