Set transformations posed difficulties for children, even when those transformations brought about no change in a one-to-one correspondence mapping. Because of their theoretical importance, we sought to probe the robustness of the findings of Experiment 4 with a larger sample, and therefore we conducted two additional experiments (see detailed procedures and results in the Appendix). In Experiment 4B, we presented the identity and substitution events to 32 subset-knowers (16 female, average age 33.96 months, 32:00–35:29) in a within-subject design. Here again, the children used the one-to-one correspondence cues to reconstruct the sets after the identity events, 2495 ms vs. 3997 ms,

F  (1, 26) = 5.6, p   = .026, ηp2=.18, but not after the substitution events, 1723 ms vs. 2301 ms, F(1,29)<1,ηp2=.021; however, this time the interaction between Condition and Set Size did not reach significance, F  (1, 24) = 1.4, Erastin order p   = .25, ηp2=.05. We then performed a third experiment (Experiment 4C), which also served to evaluate the impact of the training procedure on children’s use of branches

as cues. Twenty-four children (13 female, average age 33.98 months, 32:05–35:26) LEE011 molecular weight were tested in the same conditions as in Experiment 4, except that the last training trial, designed to attract children’s attention to the branches, was omitted. This time, the children’s longer search for a set of 6 vs. 5 puppets failed to reach significance in the identity condition, 1812 ms (5 puppets) vs. 2247 ms (6 puppets), F  (1, 11) = .33, p   = .58, ηp2=.029, while searching times for Low-density-lipoprotein receptor kinase the two sets again were equivalent in the substitution condition, 1260 ms vs. 1270 ms, F(1,11)=.04,p=.85,ηp2<.01. Again, there was no interaction between Condition and Set Size, F  (1, 22) = .35, p   = .46, ηp2=.015. We next pooled all the data together (n = 80) in a mixed-model analysis to probe the robustness of the findings and perform comparisons across experiments. This analysis accorded exactly with the original findings of Experiment 4: we obtained a main effect

of Set Size, χ2(1) = 6.8, p = .009, a main effect of Condition, χ2(1) = 8.1, p = .004, and most crucially, an interaction between these two factors, χ2(1) = 4.5, p = 0.034. None of these effects was significantly modulated by Experiment (this was also true when Experiments 4B and 4C were compared separately with Experiment 4: see Appendix). In summary, while the pooled analysis indicated that the differences observed across experiments were not statistically reliable, it provided further support for the conclusions derived from Experiment 4: children were able to use one-to-one correspondence mappings to reconstruct exact sets through identity events, but not through substitution events. In the next experiment, we return to children’s ability to reconstruct exact sets in the absence of transformations.