Responses to the Competing-units
Counting Task are shown in Table 1. Children on average counted incorrect units
on 3.11 trials (SD = 1.53) and counted
inaccurately on 1.75 (SD = 1.43) of
the eight trials of the task.
Descriptive Statistics
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---|---|---|---|---|---|---|---|---|---|
cpm | pens | counting_incorrect_units | counting_inaccuracy | ||||||
Valid | 64 | 64 | 64 | 64 | |||||
Missing | 0 | 0 | 0 | 0 | |||||
Mean | 10.469 | 16.563 | 3.109 | 1.750 | |||||
Std. Deviation | 2.987 | 4.659 | 1.534 | 1.425 | |||||
Minimum | 5.000 | 5.000 | 0.000 | 0.000 | |||||
Maximum | 18.000 | 24.000 | 6.000 | 6.000 | |||||
We calculated a Spearman correlation
matrix, shown in Table 2. There
were strong correlations between children’s numeracy skills and all other
measured variables. The number of instances in which children counted the incorrect
units was strongly negatively related to children’s general numeracy skills.
Spearman Correlations
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---|---|---|---|---|---|---|---|---|---|---|---|---|---|
age | cpm | pens | counting_incorrect_units | counting_inaccuracy | |||||||||
age | Spearman's rho | — | |||||||||||
p-value | — | ||||||||||||
cpm | Spearman's rho | 0.211 | — | ||||||||||
p-value | 0.094 | — | |||||||||||
pens | Spearman's rho | 0.414 | *** | 0.413 | *** | — | |||||||
p-value | < .001 | < .001 | — | ||||||||||
counting_incorrect_units | Spearman's rho | -0.279 | * | -0.266 | * | -0.576 | *** | — | |||||
p-value | 0.026 | 0.033 | < .001 | — | |||||||||
counting_inaccuracy | Spearman's rho | -0.303 | * | -0.426 | *** | -0.564 | *** | 0.373 | ** | — | |||
p-value | 0.015 | < .001 | < .001 | 0.002 | — | ||||||||
* p < .05, ** p < .01, *** p < .001 |
We calculated a hierarchical linear regression in order to isolate the relationship between counting of incorrect units and numeracy. We predicted children’s numeracy skills, as measured by the Preschool Early Numeracy Scale, in the first step by children’s age, intelligence and frequency of counting inaccuracies. This set of control variables explained 41.7% of variance in numeracy skills, F(3, 60) = 14.31, p <.001.
In the second step we entered counting incorrect
units scores as an additional predictor of numeracy. Counting incorrect units explained
an additional 9.0% of variance in children’s numeracy, Fchange(1,
59) = 10.82, p = .002. Moreover, counting incorrect units was the
strongest predictor in the full model
Model Summary
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Model | R | R² | Adjusted R² | RMSE | R² Change | F Change | df1 | df2 | p | ||||||||||
0 | 0.646 | 0.417 | 0.388 | 3.645 | 0.417 | 14.311 | 3 | 60 | < .001 | ||||||||||
1 | 0.712 | 0.507 | 0.474 | 3.379 | 0.090 | 10.816 | 1 | 59 | 0.002 | ||||||||||
Note. Null model includes age, cpm, counting_inaccuracy |
ANOVA
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---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Model | Sum of Squares | df | Mean Square | F | p | ||||||||
0 | Regression | 570.475 | 3 | 190.158 | 14.311 | < .001 | |||||||
Residual | 797.275 | 60 | 13.288 | ||||||||||
Total | 1367.750 | 63 | |||||||||||
1 | Regression | 693.994 | 4 | 173.499 | 15.193 | < .001 | |||||||
Residual | 673.756 | 59 | 11.420 | ||||||||||
Total | 1367.750 | 63 | |||||||||||
Note. Null model includes age, cpm, counting_inaccuracy |
Coefficients
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---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Model | Unstandardized | Standard Error | Standardized | t | p | ||||||||
0 | (Intercept) | 2.497 | 4.591 | 0.544 | 0.588 | ||||||||
age | 2.709 | 0.908 | 0.320 | 2.985 | 0.004 | ||||||||
cpm | 0.278 | 0.172 | 0.178 | 1.615 | 0.112 | ||||||||
counting_inaccuracy | -1.156 | 0.356 | -0.354 | -3.246 | 0.002 | ||||||||
1 | (Intercept) | 8.862 | 4.676 | 1.895 | 0.063 | ||||||||
age | 2.083 | 0.863 | 0.246 | 2.414 | 0.019 | ||||||||
cpm | 0.214 | 0.161 | 0.137 | 1.335 | 0.187 | ||||||||
counting_incorrect_units | -1.044 | 0.317 | -0.344 | -3.289 | 0.002 | ||||||||
counting_inaccuracy | -0.819 | 0.346 | -0.250 | -2.369 | 0.021 | ||||||||