Finally, to assess the effects of visual strategies (foil categories), visual complexity, task-order, grammar abilities and non-verbal intelligence, we used a semiparametric regression technique called Generalized Estimating Equations (GEE), a technique useful when analyzing binomial data with within-subjects effects (Hanley, 2003). We created several models containing

different variables: ‘grade’ and ‘task-order’ as between-subjects variables; ‘task’, ‘foil category’ and ‘visual complexity’ as within-subjects variables; and ‘grammar’ and ‘intelligence’ raw scores as covariates. All analyses were performed with SPSS® 19. General overview: correct responses by grade. On average, the 26 children attending the fourth grade (M = 0.80, SD = 0.21) had a significantly higher proportion of correct responses in VRT than children attending Selleckchem LDN 193189 the second grade (M = 0.59,

SD = 0.17) (Mann–Whitney U: z = −3.70, p < 0.001; Fig. 7). selleck compound Moreover, while 69.2% of fourth graders had a proportion of correct answers above chance, only 26.9% of the second graders had so. This difference was also significant (χ2 = 9.43, p = 0.002). One child in the fourth grade and one in the second grade had performance scores lower than predicted by chance (i.e. equal or lower than 26%). This means that these children discriminated recursive items from foils more than 74% of the trials, but still consistently chose the foils. These two participants were excluded from further regression and correlation analyses involving VRT because even though they induced a rule that allowed them to distinguish recursive items from foils, they would be treated as performing worse than other participants performing randomly. Since

Mirabegron we were interested in investigating the cognitive underpinnings of the ability to represent recursion, these two subjects would be ambiguous and noisy data points. 2 Visual strategies. A central issue concerning our method is the question of whether participants were able to represent the structural self-similarity present in the recursive images; and to apply this knowledge throughout different VRT trials. One possible alternative to the representation of self-similarity would be the usage of heuristic strategies, based on the detection of simple salient features within the foils, which would allow their exclusion without an understanding of the underlying structure. In order to prevent the emergence of a systematic ‘choice-by-exclusion’ strategy, we used different categories of foils. Our assumption was that, if individuals were able to represent self-similarity, they would perform adequately in all different foil categories. At the group level, the number of correct choices was significantly above chance for all foil categories and for both grade groups (Binomial test, p < 0.005). For detailed analyses comparing performance across categories see Appendix C. Visual complexity.