Brinley Plot Analysis of Choice RT Studies

Supplementary Materials for “Decision processes and the slowing of simple choices in schizophrenia”

Brinley Plot Analysis of Choice RT Studies

In the domain of aging, Cerella(1994) inferred general slowing from a strong linear relationship (r2 = .89) in a Brinley plot, with a slope of 1.35 in plots of young- against old-participant RT. Schatz (1998) reported similar findings with control RT explaining 87% of the variance in the schizophrenia group’s RT. He divided tasks into lexical, non-lexical and inhibitory types and reported slopes of 1.75, 1.39 and 2.3 respectively, but noted differentiating tasks only added marginally to the variance explained.

Note, however, that since Schatz’s (1998) work, it has been shown that Brinley plot slopes do not indicate anything about general slowing, but rather are influenced by difference inRT standard deviations (Ratcliff et al., 2000). Ratcliff et al. showed that a regression analysis of a Brinley plot is relatively uninformative (see also Cerella, 1994), with a slope greater than one having multiple potential causes. For example, it is consistent with a DDM with either a higher response threshold or a slower evidence accumulation rate for old compared to young participants. Ratcliff et al. recommend a DDM analysis be used instead of Brinley plots because it provides a qualitatively deeper understanding of the cognitive mechanism that mediates aging effects.

Subsequently, Ratcliff and colleagues followed up this recommendation in a wide-ranging series of studies (Ratcliff, Love & Opfer, 2011; Ratcliff, ThaparMcKoon, 2001, 2003, 2004, 2006a,2006b, 2007, 2010, 2011; Ratcliff, Thapar, Gómez & McKoon, 2004; Thapar, Ratcliff & McKoon, 2003). Theyconsistently showed that – apart from a few cases in perceptual choice where aging caused sensory degradation– age does not affect the rate of evidence accumulation. Rather, slowing occurs because older participants set a higher threshold (i.e., they trade speed for accuracy), and to a lesser degree due to a slowing in non-decision time by 0.05-0.1s. Previously, it had been widely assumed that age-related slowing had a single cause; a general reduction in the rate of information processing. These findings suggest that the results of Schatz’s (1988) Brinley plot analysis do not necessarily indicate a slowing in the rate of information processing in schizophrenia.

We added to the list of studies provided by Schatz (1988) by searching thePsychInfo and Medline databases using the term "schizophrenia" combined separately with "reaction time", "lexical", "semantic", and "inhibition", selecting articles published during 1996 - 2014. Together both sources yielded 83 papers (see references at the end of this section) that reported 317 conditions with numerical results for one or more of average correct RT (i.e., the mean or median RT for correct responses) and accuracy for both schizophrenia and control groups. We were also interested in the difference in RT standard deviations implied by the slopes greater than one reported by Schatz, so we also recorded the mean of individual participant’s correct RT standard deviation where available.

The variety of tasks in our set of papers was very similar to Schatz’s (1998) sample, except that simple RT tasks were excluded. Following Schatz, tasks were classified inhibitory (e.g., Stroop: 180 conditions), lexical (i.e., decisions about words, 67 conditions) and non-lexical (i.e., perceptual decisions, 70 conditions). Overall, mean RT results were reported for 314 conditions (179 inhibition, 67 lexical, 68 non-lexical), accuracy for 189 conditions (118 inhibition, 35 lexical, 36 non-lexical), and standard deviations for 9 conditions (5 inhibition, 2 lexical, 2 non-lexical).

Given the small number of observations available, we did not break the standard deviations down by task type. Despite the small sample size, the average standard deviation for patients (0.140s) was significantly greater than for controls (0.099s), t(8) = 12, p < .001, by a factor very similar to that indicated by the slope in Schatz’s analysis. The difference between groups in RT means and standard deviations was almost exactly equal (.042 vs. .041s), and proportionally the standard deviation difference was larger (1.44 vs. 1.09), in the seven cases that reported both.

Overall, the controls (0.67s) were significantly faster than the patients (0.91s), t(313) = 17.5, p < .001, and this was true separately for the inhibition (0.6s vs. 0.79s), t(178) = 14.1, p < .001, lexical (0.7s vs. 0.92s), t(66) = 8.9, p < .001, and non-lexical (0.83s vs. 0.123s), t(67) = 9.5, p < .001, task groups. There was one large outlying inhibition-task result (Schneider, 2011), but there was little effect on the group difference when it was removed (0.58s vs. 0.76s), t(66) = 16.5, p < .001.

The right panel of Figure 1 shows that accuracy was close to ceiling in most cases; averaged over groups, 72% of conditions had accuracy greater than 95% and 87% of conditions with average accuracy greater than 90%. However, the cases in which patients were more accurate were not due to ceiling effects as they were more prevalent in lower accuracy conditions (19% and 24% for conditions with less than 95% and 90% average accuracy respectively).

Overall, the controls (96.6%) were significantly more accurate than the patients (94.2%), t(188) = 7.7, p < .001, and again this was true separately for the inhibition (96.4% vs. 94.4%), t(117) = 6.2, p < .001, lexical (96.6% vs. 93.7%), t(34) = 4.3, p < .001, and non-lexical (97.2% vs. 94.2%), t(35) = 3, p = .005, tasks. Similar results were obtained when conditions near ceiling (average accuracy greater than 95%)were removed: both overall (91.3% vs. 86%), t(52) = 6, p < .001, and for the inhibition (90.8% vs. 87.6%), t(32) = 3.2, p = .003, lexical (92.1% vs. 84.3%), t(9) = 7.2, p < .001, and non-lexical (92.6% vs. 92%), t(9) = 33.6, p = .006, tasks.

The general findings reported so far are not consistent with slowing being due to a speed-accuracy trade-off (i.e., slowing was not uniformly associated with greater accuracy). To quantify this pattern we calculated the correlation of the patient minus control group average RT differences with the corresponding accuracy differences, where speed-accuracy trade-offpredicts a positive value. There wasa good number of cases, 188, where the required results were available.The resulting correlation was negative but small, r = -0.09, and non-significant, t(186) = 1.3, p = .2. The weak correlation was not due to the large number of conditions near ceiling: when cases with greater than 95% average accuracy were removed the correlation weakened, r = .06, t(51) = 0.46, p = 0.65.

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