3.1. Descriptive Statistics and Analyses of Differences between Age Groups and Sexes
gives an overview of the main test variables with descriptive statistics across age groups, for boys, and girls. Abbreviated variable names will be used in the following, as defined in the subheadings of Section 2.3
. As expected, performance on CubeRotPC was lower than on GhostRotPC, which was originally designed for adults (pairwise t
-tests for the total sample: t
(95) = 21.89, p
< .001; for single age groups: all t
s > 7.94, all p
s < .001). In fact, there were only two children in the entire sample who had a (minimally) higher score on CubeRotPC than on GhostRotPC. A similar pattern emerged for the paper–pencil tasks. Both in absolute terms (see Table 1
(95) = 12.92, p
< .001) and in percentage, average results were higher on GhostRotPP than on FigureRotPP.
In order to facilitate the analysis and comparison of age trends, participants’ scores on the five spatial tasks were z-standardized. As evident in Figure 5
, performance on MR tasks increased sharply between 7 and 8 years of age but plateaued thereafter. In contrast, PerspectivePC performance improved almost linearly with increasing age, and still showed substantial progress between 8 and 9 years of age. These observations were tested for statistical significance by means of separate two-way analysis of variance (SS type II) for each task, with age and sex as independent variables. A square-root transformation was applied to PerspectivePC scores and CubeRotPC scores in order to meet the requirements of normally distributed residuals and variance homogeneity. Significant age effects were found for GhostRotPC, FigureRotPP, GhostRotPP, and PerspectivePC (all F
s > 7.60, all p
s <.001, all ηg2
> .232) but only a nonsignificant trend for CubeRotPC, F
(3, 88) = 2.40, p
= .073, ηg2
= .076. Post hoc Welch’s t
-tests comparing consecutive age groups showed significant differences between 7- and 8-year-olds for all MR tasks (all t
> 2.03, all p
s < .002), including CubeRotPC, t
(45) = 2.03, p
= .048. No other age differences were significant for the five MR tasks (all t
s < 1.55, all p
s > .130). PerspectivePC performance, on the other hand, increased between 6 and 7 years of age, t
(42) = 3.65, p
< .001, as well as between 8 and 9 years, t
(49) = 2.19, p
= .033, but not between 7 and 8 years, t
(43) = 1.40, p
= .169. No significant sex differences were found for the spatial tasks (all F
s < 1.17, all p
s > .282, all ηg2
< .013), except for GhostRotPC, which showed a significantly higher performance for boys than for girls, F
(1, 88) = 7.61, p
= .007, ηg2
= .080. The ANOVAs revealed no significant interactions between sex and age (all F
s < 1.74, all p
s > .165, all ηg2
Separate age by sex ANOVAs were also calculated for the hours spent with TV and Games as dependent variables. A logarithmic transformation was applied to both variables in order to meet ANOVA requirements. Neither TV, F(3, 87) = 0.95, p = .420, ηg2 = .032, nor Games, F(3, 63) = 0.95, p = .422, ηg2 = .043, showed significant age differences. For Games, a significant effect of sex could be observed, F(1, 63) = 7.9, p = .016, ηg2 = .088, with boys playing more hours per week than girls. No significant interactions of age and sex were found (all Fs < 1.58, all ps > .202, all ηg2 < .070).
Even after transformation, SES did not fulfill the ANOVA’s requirement of homogeneity of variances. Hence, only Walsh’s t-tests (which are relatively robust against unequal variances) were calculated for both main effects. Girls’ and boys’ parental SES did not differ, t(33) = −0.26, p = .792. No differences in parental SES between consecutive age groups were observed (all ts < .47, all ps > .642), with the exception of a significant difference between 8- and 9-years-olds, t(33) = 2.12, p = .042.
For the Verbal-IQ T-Scores, no age differences were to be expected due to T-scores being age-normalized. Accordingly, the ANOVA revealed no significant effect of age, F(3, 88) = 1.62, p = .191, ηg2 = .052. Moreover, there was no significant effect of sex, F(1, 88) = 0.70, p = .191, ηg2 = .008, and no interaction, F(3, 88) = 0.48, p = .016, ηg2 = .696.
3.3. Correlations among Tasks
Pearson correlations and partial correlations controlled for age (in months) were calculated for each pair of variables. Again, logarithmic and square-root transformations were applied to Games, TV, PerspectivePC, and CubeRotPC values to achieve normally distributed data. Table 3
shows the Pearson correlations (below the diagonal) and partial correlations (controlled for age; above the diagonal) between all variables, as well as significance levels that were Bonferroni–Holm-corrected for multiple testing, respectively.
Among the four MR scores, correlation coefficients were all statistically significant with medium to large effect sizes, except for the correlation between CubeRotPC and GhostRotPP. Even though these coefficients were reduced in size after controlling for age, the general pattern remained the same. Correlations between the four MR scores and PerspectivePC were smaller in comparison, and when age was controlled for, none of the correlations remained significant. The correlation between PerspectivePC and the CubeRotPC was even close to zero.
A rather irregular pattern emerged for the (partial) correlations between spatial and nonspatial scores. None of the nonspatial variables were significantly related to CubeRotPC performance. TV consumption was, albeit not statistically significant, negatively associated with MR scores, with small but consistent negative relations. Games, on the other hand, showed a less consistent pattern.
Verbal-IQ scores showed weak- to medium-sized correlations with spatial abilities, with the exception of CubeRotPC. The paper–pencil tasks and PerspectivePC were also positively related to SES. However, these correlations were not statistically significant when age was controlled. When age-controlled, SES and Verbal-IQ were both negatively but not significantly related to TV consumption and (to a lesser extent) to Gaming.
3.4. Maximum-Likelihood Exploratory Factor Analyses
To obtain a fuller picture of the relations among the five spatial task scores, a factor analysis was conducted based on age-controlled partial correlations. The Kaiser criterion and Scree plot indicated only a single factor for a maximum-likelihood factor analysis, whereas parallel analysis suggested two factors. Hence, two separate analyses were conducted: one for a single-factor solution and one for a two-factor solution with oblique rotation. Factor loadings for both analyses are presented in Table 4
. The single-factor solution accounted for 37% of the total variance (RMSEA = .054, χ2
(5) = 6.43, p
= .266). The two-factor solution accounted for 55% of the total variance (Factor 1: 34%, Factor 2: 21%; RMSEA < .01, χ2
(1) = 0.28, p
= .594). In both analyses, the first factor was primarily related to FigureRotPP, GhostRotPP, and GhostRotPC. CubeRotPC loaded moderately on the single factor. In the two-factor solution, on the other hand, CubeRotPC alone constituted the second factor. The two factors correlated with r
= .32, which was nearly identical to the factor loading of CubeRotPC in the single-factor solution. GhostRotPC also showed weak cross-loadings on the second factor. Finally, PerspectivePC was always associated with the first factor, albeit only weakly.
Due to the above findings that some spatial scores were strongly related to verbal abilities, the two-factor analyses were repeated, including partial correlations with Verbal-IQ scores. The single-factor solution accounted for 32% of the total variance (RMSEA = .067, χ2
(9) = 12.99, p
= .163) and the two-factor solution for a little over 43% (Factor 1: 30%, Factor 2: 13%; RMSEA = .05, χ2
(4) = 5.00, p
= .288), with an interfactor correlation of r
= .37. Factor loadings for both analyses are presented in Table 5
. Most importantly, the pattern of factor loadings was nearly identical to the one obtained without Verbal-IQ. Again, the first factor was weakly associated with PerspectivePC and most strongly related to FigureRotPP, GhostRotPP, and GhostRotPC. CubeRotPC was moderately associated with the first factor (single-factor solution) or the main contributor to the second factor (two-factor solution). Again, GhostRotPC showed weak cross-loadings on the second factor. Verbal-IQ loaded moderately on the first factor in both solutions and was negatively related (but weakly) to the second factor in the two-factor solution.
3.5. Response Times
In addition to the performance score used as an index of each individual child’s average performance, computer tasks also offer the possibility to analyze performance on trial-by-trial basis. As is typical for computerized MR tasks, response times were analyzed as a function of angle of presentation (i.e., the angular discrepancy between the presented stimulus and its upright reference figure). Response times for incorrect trials were included in order to have more data points (the same number as used for the above performance score), and average response times were highly similar with and without the incorrectly solved trials (Pearson’s r
= .94, p
< .001 for CubeRotPC, and r
= .98, p
< .001 for GhostRotPC). Mean response times by angle and age group are presented in Table 6
(GhostRotPC) and Table 7
(CubeRotPC). Overall, children responded faster on GhostRotPC than on CubeRotPC, t
(95) = 12.84, p
An ANOVA with response times on GhostRotPC as dependent variable, the within-participant variable of angle (7), and the between-participant variable of age group (4) yielded significant main effects of angle, F(4, 358) = 23.43, p < .001, ηg2 = .089, and age group, F(3, 92) = 3.35, p = .023, ηg2 = .063, but no interaction, F(12, 358) = 0.88, p = .570, ηg2 = .011.
An analogous ANOVA with response times on CubeRotPC as dependent variable, the within-participant variable of angle (5), and the between-participant variable of age group (4) yielded a significant effect of angle, F(3, 253) = 83.75, p < .001, ηg2 = .294, but no effect of age group, F(3, 92) = 0.10, p = .958, ηg2 = .002, and no interaction, F(8, 253) = 1.27, p = .259, ηg2 = .019.