15.1.1. Diffusion model comparisons between experiments 5 and 6
Correlations for diffusion model parameters between experiments 5 and 6 are reported by group in table 15.1. One often-discussed strength of the diffusion model is that a given model parameter tends to correlate fairly well across experiments, but correlate poorly with other parameters within the same experiment (e.g., Ratcliff & McKoon, 2008). When combined with the fact that model parameters tend to be
differentially sensitive to various experimental manipulations (e.g., stimuli proportions on response bias, word frequency effects on drift rates), this is interpreted to mean that model parameters truly reflect basic aspects of the decision process.
As an example of cross-experiment correlation relevant to the current work, Ratcliff et al. (2010) reported correlations between a lexical decision and numerosity in a sample of old and young participants at r =.33 for boundary width, .47 for nondecision time, and .47 for drift rate. Averaging across task type by group, correlations in the current experiment are roughly in the same range for boundary width (MC r = .37; PWA r = .55) and non-decision time for both groups (MC r = .24; PWA r = .63), but not for drift rate (MC r = .06; PWA r = .07). Although it was predicted that drift rates would differ across experiments for PWA given the differences in lexical processing involved, this was not predicted for MCs, and the source of this difference is unclear. It may be related to shifts in speed and accuracy focus, as the drift rate correlations for MCs in the neutral condition had a more expected average correlation (r = .47).
Table 15.1. Correlations between diffusion parameters for experiment 5: Lexical Decision, and Experiment 6: Numerosity Judgment, separately by group.
Parameter Condition PWA MC
zr Neutral -0.01 0.35 . Accuracy 0.14 0.04 . Speed 0.08 0.19 szr . 0.30 0.47 a Neutral 0.69 0.11 . Accuracy 0.50 0.62 . Speed 0.47 0.38 t0 Neutral 0.62 0.42 . Accuracy 0.63 0.11 . Speed 0.65 0.19 st0 . 0.49 -0.09 v Neutral: HighEasy/ HF 0.16 0.53 . Neutral: HighHard/ LF -0.02 0.41 . Accuracy: HighEasy/ HF 0.15 -0.18 . Accuracy: HighHard/ LF -0.08 0.15 . Speed: HighEasy/ HF 0.08 -0.26 . Speed: HighHard/ LF 0.14 -0.32 sv . 0.51 -0.20 p . 0.06 0.52
Note: correlations between experiments for lower boundary drift rate responses not reported due to qualitative differences in stimuli.
Diffusion model differences were evaluated between experiments for the parameters v, a, and t0 in a set of 3-way repeated measures ANOVAs. Analysis of v crossed stimulus condition for the upper bound responses (HF words/Large Easy
numerosity vs. LF words /Large Hard numerosity), experiment domain (lexical decision vs. numerosity), and group, while analyses for a and t0 crossed task condition, experiment domain, and group (table 15.2).
interactions between group and stimulus condition, such that PWA showed less of a difference between easy and hard stimuli across domain types (p = 0.01), and between group and domain, such that MC presented with higher drift rates in lexical decision compared to numerosity, but PWA did not differ between domains.
For a, there were main effects of group, with PWA setting more conservative criteria overall, and of task (ps < 0.01), but no effects of domain, and no interactions involving group (ps > 0.05). However, there was a two-way interactions between task and domain, and post-hoc pairwise testing revealed a larger difference between speed and accuracy focused conditions in numerosity comparison to lexical decision that was marginally significant (p = 0.08). Although the separate experiment analyses reported a significant interaction between group and task in lexical decision and no such relationship in numerosity judgment, the difference between these does not appear to be significant when tested directly, and boundary widths in the numerosity task show the same general trends without reaching significance.
For t0, there was a 3-way interaction between group, task, and domain (p = 0.002). Post-hoc comparisons of the constituent 2-way interactions revealed that this interaction was driven by differences in the neutral condition for MCs between experiments, who showed no differences between neutral and accuracy focused conditions in lexical decision, but were faster in neutral compared to accuracy focused conditions in
numerosity (p = 0.018; figure 15.1). In terms of the 2-way task by group interactions on t0 reported separately in both experiments 5 and 6, the effect was only marginally
differences in the neutral condition between experiments washing out group effects; a secondary model looking specifically at group differences in the speed vs. accuracy conditions in a separate ANOVA collapsing across experiment showed the crucial task adaption effect previously reported: F(1, 41) = 7.067, p = . 011, ηp2 =.02.
Table 15.2. ANOVA comparisons of group, domain, and condition for experiments 5 and 6 on drift rate parameters.
DFn DFd F p<.05 ηp2 15.2.1 Drift rate (v) Group 1 41 15.74 <0.001* 0.17 StimType 1 41 306.29 <0.001* 0.46 Domain 1 41 68.85 <0.001* 0.33 group: StimType 1 41 4.53 0.039* 0.01 group: Domain 1 41 7.37 0.010* 0.05 StimType: Domain 1 41 0.71 0.404 0.00
group: StimType: Domain 1 41 0.38 0.54 0.00
15.2.2 Boundary width (a)
group 1 41 7.42 0.009* 0.08 Task 2 82 68.16 <0.001* 0.28 Domain 1 41 1.59 0.215 0.01 group: Task 2 82 1.80 0.173 0.01 group: Domain 1 41 0.17 0.679 0.00 Task: Domain 2 82 5.45 0.006* 0.01
group: Task: Domain 2 82 1.98 0.144 0.01
15.2.3 Nondecision time (t0) group 1 41 8.52 0.006* 0.10 Task 2 82 2.62 0.079 0.01 Domain 1 41 2.55 0.118 0.02 group: Task 2 82 2.65 0.076 0.01 group: Domain 1 41 0.52 0.477 0.00 Task: Domain 2 82 2.84 0.064 0.01
Figure 15.1. Comparisons of group, domain, and task for experiment 5 (left) and experiment 6 (right) on nondecision times t0.
Error bars represent ± 1 standard deviation.
Experiment 5: Lexical Decision Experiment 6: Numerosity Judgment
15.1.2. Effects of executive attention on experiments 5 and 6.
It was predicted that generating and maintaining speed and accuracy priorities in response to varying task constraints required task maintenance, and that any group differences in task adaption would be attributable to differences in this aspect of executive attention. This hypothesis was tested using ANCOVAs focusing on
nondecision time performance collapsing across experiments, given the fact that this is where group differences in task adaption were found to occur. ANCOVAs were run testing for the interaction between group and task instruction (speed vs. accuracy) when controlling for individual differences in task maintenance. Task maintenance was measured via the differences scores reported in chapter 12, and two versions of this ANCOVA were evaluated; one that partialed out task maintenance ability based on performance in the SART experiments 1 and 2, and one that partialed out performance on
model parsimony, and also due to the notably divergent patterns of impairments between these task types reported in Chapter 12 (PWA who showed impairment in one SART task tended to show impairment on the other, but not on either Stroop task, and vice versa). Neither of these ANCOVAs mediated the task by group interaction on nondecision times (ps < 0.01), indicating that group differences in non-decision times we’re not due to differences in task maintenance.
Previous work has reported some effects of working memory and fluid
intelligence on drift rate (e.g., Ratcliff et al., 2010; Schmiedek et al., 2007). Given group differences in drift rates and the theoretical relationship between executive attention, working memory, and fluid intelligence (Engle and Kane, 2004), the above ANCOVA approach was also employed to determine if these measures mitigated group differences in drift rate as well. Again, two ANCOVAs were run, partialling out SART and Stroop- related task maintenance while testing for the interaction between group and stimuli type on drift rates reported in table 15.2. However, the significant interaction term remained unchanged in both models (ps < 0.05), indicating that group differences and drift rate processing were not due to task maintenance deficits.