As before, we measured both the RT and error rates, and the results are plotted by the number of objects shown in the small set (
Figure 4a) and by the object ratio (
Figures 4b and
4c). Also, see the mean and standard deviation for both RT and error rates for each full object ratio and stimulus duration in
Table 3.
Replicating the results of
Experiments 1 and
2, we again found that RT was significantly faster both for a more disparate ratio,
F(1,11) = 32.82,
p < 0.001, η
2P = 0.74, and when more objects were included in a trial,
F(1,11) = 28.63,
p < 0.001, η
2P = 0.72 (
Figure 4a). Unlike in
Experiment 2, where we did not see a main effect of presentation duration in RT, here the longer presentation duration led to a slower RT,
F(1,11) = 13.44,
p < 0.01, η
2P = 0.55. There was also an interaction between ratio and object numerosity,
F(1,11) = 10.05,
p < 0.01, η
2P = 0.47. Pairwise
t-tests revealed that, when ratio was fixed, the RT was faster when object numerosity was high,
ts > 6.44,
ps < 0.001,
ds > 1.31 (corrected), but the effect seemed to be somewhat more pronounced for the 2:3 ratio (
d = 1.33) than the 1:2 ratio (
d = 1.31). There was no two-way interaction between numerosity and presentation duration,
F(1,11) = 1.03,
p = 0.33, η
2P = 0.08, or between ratio and presentation duration,
F(1,11) = 0.96,
p = 0.34, η
2P = 0.08, and no three-way interaction among all three factors,
F(1,11) = 0.46,
p = 0.51, η
2P = 0.04.
As in
Experiment 2, when comparing the RTs of the two pairs of trials with the same object ratio and total presentation duration but different numerosities, we found that when combining both cases, trials with more objects had a significantly faster RT,
t(11) = 5.10,
p < 0.001,
d = 1.47. These results were further confirmed when each pair was analyzed separately,
ts > 4.50,
ps < 0.001,
ds > 1.30 (
Figure 4b).
As before, to understand if a difference in ratio still played a role when the absolute difference between the two sets was fixed, we also compared RT differences between 2 versus 4 (at a ratio of 1:2) and 4 versus 6 (at a ratio of 2:3). We found that there was no significant difference in RT for the 2 versus 4 and 4 versus 6 conditions,
t(11) = 2.02,
p = 0.068,
d = 0.58 (
Figure 4c), although there was a trend of a more disparate ratio resulting in a slower RT, similar to the results from
Experiments 1 and
2.
As in
Experiment 2, in error rate measures, we observed both an effect of ratio, with a lower error rate for a more disparate ratio,
F(1,11) = 299.29,
p < 0.001, η
2P = 0.96, and an effect of numerosity, with lower error rate when more objects were shown in a trial,
F(1,11) = 21.17,
p < 0.001, η
2P = 0.65 (
Figure 4a). There was no significant effect of stimulus duration on error rate,
F(1,11) = 4.37,
p = 0.06, η
2P = 0.28. There was no two-way interaction between numerosity and ratio,
F(1,11) = 0.06,
p = 0.81, η
2P = 0.005, between numerosity and presentation duration,
F(1,11) = 0.16,
p = 0.69, η
2P = 0.014, or between ratio and presentation duration,
F(1,11) = 1.19,
p = 0.29, η
2P = 0.09, and no three-way interaction among all three factors,
F(1,11) = 0.006,
p = 0.94, η
2P = 0.0005.
When comparing the error rate of trials with the same total presentation duration and ratio of objects but different numerosities, we found no effect on the number of objects on accuracy,
t(11) = 1.45,
p = 0.176,
d = 0.42, and this was confirmed for each pair separately (
ts < 1.72,
ps > 0.22,
ds < 0.49 (corrected) (
Figure 4b).
As in the RT analysis, we also examined the effect of ratio when the absolute difference between the two sets was fixed. We found that when the absolute difference between the two sets was fixed to 2, 2 versus 4 had a lower error rate than 4 versus 6,
t(11) = 3.92,
p < 0.01,
d = 1.13 (
Figure 4c).
Overall, these results replicated those of
Experiments 1 and
2 by showing that both the relative number (ratio) and the absolute number (numerosity) of objects included in a temporal sequence affected participants’ speed and accuracy in comparative number judgment. Moreover, these results showed that, even when total trial duration was equated and when participants could not prepare their motor responses earlier in the trials, we still found a strong effect of object numerosity in RT. The effect on the error rate was much weaker or nonexistent. When the absolute difference between two sets was fixed to 2, a more disparate ratio resulted in a higher accuracy. However, although nonsignificant, we did see an opposite trend on RT, with a more disparate ratio resulting in a slower RT. This finding is consistent with the pattern of results found in
Experiments 1 and
2.