Descriptive statistics for the principal measures are provided in Table 1. Group comparisons were conducted using t-tests; significance levels and effect size values (Cohen’s d) are also shown. There were significant group differences between the two groups across all measures of executive function.
Table 1. Descriptive statistics for executive function measures as a function of group
|ADHD||Comparison||Comparison and ADHD|
|Trail Making test||visual scanning time||80||11.18||2.86||50||11.84||2.71||1.25||0.22||0.22|
|motor speed time||80||10.73||2.73||50||11.16||2.51||0.80||0.43||0.14|
|number sequencing time||80||9.91||3.33||50||10.58||2.94||1.02||0.31||0.18|
|number sequencing errors||80||90.75||23.08||50||97.10||15.20||1.91||0.06||0.31|
|letter sequencing time||80||9.19||3.70||50||9.92||2.99||1.38||0.17||0.25|
|letter sequencing errors||80||76.75||29.61||50||88.98||27.50||2.41||0.02||0.42|
|number-letter sequencing time||80||10.51||2.85||50||10.56||2.92||0.09||0.93||0.02|
|number-letter sequencing errors||80||32.86||22.38||50||45.51||18.30||3.51||0.00||0.58|
| Interference test||color naming time||77||10.25||2.99||49||12.20||3.45||3.62||0.00||0.62|
|color naming errors||77||47.19||37.31||49||73.27||35.70||4.27||0.00||0.72|
|word reading time||77||9.88||3.29||49||12.16||2.14||4.99||0.00||0.75|
|word reading errors||77||54.84||44.67||49||82.45||33.40||4.44||0.00||0.70|
|color-word with switch time||77||10.55||3.25||49||12.29||2.87||3.07||0.00||0.54|
|color-word with switch errors||77||41.49||24.53||49||53.37||20.30||4.58||0.00||0.78|
|Card Sort test||number of free sorts||83||5.71||2.49||50||7.86||2.26||4.99||0.00||0.82|
|Tower test||total achievement||83||13.95||4.80||50||12.94||3.83||1.34||0.18||0.23|
| Performance test||omissions||83||34.39||23.07||50||23.36||21.20||2.75||0.01||0.48|
|Response inhibition||walk / don’t walk||83||3.83||3.31||50||9.28||3.69||8.80||0.00||1.25|
|Working memory||verbal STM||83||98.82||16.81||50||112.3||10.2||5.11||0.00||0.84|
The ADHD group committed significantly more errors in three conditions of the Trail Making test: Number Sequencing, Letter Sequencing and Number-Letter Sequencing. However, there were no significant differences between the groups in terms of completion time in these conditions, nor were there any significant differences in the Visual Scanning or Motor Speed conditions of this test.
The ADHD group also committed significantly more errors than the non-ADHD group in all conditions of the Color-Word Interference test: the Word Reading, Color Naming, Color-Word and Color-Word with Switch conditions. The non-ADHD group performed each of these conditions significantly faster than the ADHD group, but the completion times of the ADHD group still fell within the normal range.
On the Tower test, the groups did not differ significantly on total achievement score, indicating that there were no significant differences in the number of moves taken to complete the task. However, the ADHD group committed a significantly greater number of rule violations than the non-ADHD group.
The ADHD group was also significantly impaired on the Card Sort test relative to the non-ADHD group, demonstrating poorer problem-solving and conceptual skills. They also committed a significantly greater number of both omissions and commissions on the CPT than the non-ADHD children.
Finally, the ADHD group scored significantly more poorly than the non-ADHD group across all four aspects of WM; verbal STM, visuo-spatial STM, verbal WM and visuo-spatial WM. These differences were significant for all 12 WM subtests.
Discriminant function analyses were conducted to evaluate the extent to which performance on executive function measures accurately predicted whether children had been diagnosed with ADHD or not. In the first analysis, all of the principal executive function measures were entered. The resulting function was significant, Λ =.40, χ2 (26, N = 126) = 100.57, p < .001. Canonical variate correlation coefficients for this function are shown in Table 2. Group membership was classified correctly for 85.7% of the children, with 88.3% of the ADHD and 81.6% of the comparison children correctly assigned. With leave-one-out cross validation, a method that assesses the extent to which the function can predict a new sample, 77.8% of the sample were correctly classified, 80.5% of the ADHD and 73.5% of the comparison children. Acceptable levels of classification range between 70% and 90% (Glascoe & Squires, 2007; Miesels, 1988).
Table 2. Canonical variate correlations
|Trail Making test||visual scanning time||0.09|
|motor speed time||0.06|
|number sequencing time||0.06|
|number sequencing errors||0.09|
|letter sequencing time||0.08|
|letter sequencing errors||0.16|
|number-letter sequencing time||0.01|
|number-letter sequencing errors||0.25|
| Interference test||color naming time||0.25|
|color naming errors||0.29|
|word reading time||0.32|
|word reading errors||0.27|
|color-word with switch time||0.23|
|color-word with switch errors||0.37|
|Card Sort test||number of free sorts||0.33|
|Tower test||total achievement||−0.09|
| Performance test||omissions||−0.18|
|Response inhibition||walk / don’t walk||0.62|
|Working memory||verbal STM||0.34|
The classification rates from the discriminant function analyses reported above were used to compute likelihood ratios (Sackett et al., 1991), which quantify the extent to which members of one group are more likely to score either above or below a particular cut-off value (in this case, derived from a discriminant function analysis) than members of another group. For this study, the positive likelihood ratio LR+ is calculated by dividing the proportion of children with ADHD who were correctly classified by the discriminant function as belonging to that group by the proportion of children from the comparison group who were misclassified as belonging to the ADHD group. The negative likelihood ratio LR- is obtained by dividing the proportion of children in with ADHD who were wrongly classified as belonging to the comparison group divided by the proportion of comparison group children who were correctly classified as such. The LR+ value was 4.58, indicating that children with ADHD were at least 4.5 times more likely to score poorly on executive function measures than children without ADHD. The LR- value was .14. The diagnostic odds ratio LR+/LR-, a summary measure of the degree of discrimination between the groups provided by the executive function measures, was 34.29. Diagnostic odds ratios range from 0 to infinity; values over 1 indicate that a test discriminates between groups, with higher diagnostic odds ratios indicating better discriminant ability.
These data clearly establish that multiple executive function measures can reliably discriminate between children with and without ADHD. However, their utility for clinical practice may be severely limited by the number of cognitive tests that can be undertaken in a single assessment - together, these tests take approximately 90 minutes to administer. To address this practical issue, we sought to identify the measures that provided the best individual predictors of group membership, guided by the canonical variate correlation coefficients for the first discriminant analysis. These coefficients represent the relative contribution of each dependent variable to group separation: the larger the value, the greater the contribution. The four variables with the highest coefficients were response inhibition (.62), visuo-spatial WM (.46), verbal WM (.46) and visuo-spatial STM (.44). These four variables were entered into the second discriminant analysis, Λ =.52, χ2 (4, N = 132) = 83.70, p < .001. The classification function correctly predicted group membership for 82% of the sample, with 85.56% of the ADHD group and 76% of the non-ADHD group correctly classified. With leave-one-out cross validation, the classification function was unchanged. The LR+ was 3.56 and the LR- was .19, yielding a diagnostic odds ratio of 18.74, again providing excellent group differentiation.
Separate discriminant function analyses were run for each of the four variables entered into the previous analysis to explore how useful a single measure might be at discriminating between ADHD and non-ADHD groups. The visuo-spatial WM measure was entered into the first of these analyses, Λ = .74, χ2 (1, N = 132) = 38.69, p < .001. This function correctly classified 74.4% of the sample, with 84.3% of the ADHD group and 58% of the non-ADHD group correctly identified. The classification function was unchanged with leave-one-out cross validation. The LR+ was 2.01 and the LR- was .03, yielding a diagnostic odds ratio of 67. When entered as a single predictor, the verbal WM measure, Λ = .74, χ2 (1, N = 132) = 39.01, p < .001, correctly predicted group membership for 71.4% of the sample; 77.1% of the ADHD and 62% of the non-ADHD group. The LR+ was 2.03, the LR- was .37 and the diagnostic odds ratio was 5.49 for this function, demonstrating that the verbal WM measure was not as good as a single predictor as the visuo-spatial WM measure. The next analysis, conducted on the visuo-spatial STM measure, Λ = .74, χ2 (1, N = 132) = 38.69, p < .001, revealed that it was better than the verbal WM, but poorer than the visuo-spatial WM measure, at predicting group membership for the ADHD group (81.9% were correctly classified). However, this measure yielded a high LR-, 1.52, which produced very low diagnostic odds ratio of 1.17, indicating that it is not as good overall at discriminating between the groups as the WM measures.
The final discrimination function analysis was performed on the best predictor of group membership in this dataset, response inhibition (see Table 2). The resulting function, Λ = .63, χ2 (1, N = 133) = 60.65, p < .001, correctly predicted group membership for 78.2% of the sample, with 83.1% of the ADHD and 70% of the non-ADHD groups correctly classified, yielding LR+ =2.77 and LR- =.24, and a diagnostic odds ratio of 11.54.
Taken together, this series of analyses shows that the response inhibition and visuo-spatial WM measures were the best single predictors of ADHD group membership (response inhibition, 83.1% and visuo-spatial WM, 84.3%), but that the response inhibition task was better at predicting non-ADHD group membership (response inhibition, 70%, visuo-spatial WM, 58%).