Elsevier

Intelligence

Volume 36, Issue 1, January–February 2008, Pages 10-17
Intelligence

A diffusion model explanation of the worst performance rule for reaction time and IQ

https://doi.org/10.1016/j.intell.2006.12.002Get rights and content

Abstract

The worst performance rule for cognitive tasks [Coyle, T.R. (2003). IQ, the worst performance rule, and Spearman's law: A reanalysis and extension. Intelligence, 31, 567–587] in which reaction time is measured is the result that IQ scores correlate better with longer (i.e., 0.7 and 0.9 quantile) reaction times than shorter (i.e., 0.1 and 0.3 quantile) reaction times. We show that this pattern of correlations can be predicted by the diffusion model [Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59–108], in two ways: either assuming that the rate of accumulation of information toward a decision is higher for higher IQ subjects or assuming that the criterial amounts of information they require before a decision are lower. Importantly, the model explains both reaction times and accuracy, so the two possibilities can be distinguished.

Section snippets

IQ and the diffusion model

To model how IQ affects RT, we examined how IQ might be related to one or more processing components of the diffusion model. If IQ were related to drift rate, an obvious possibility, people with higher IQ's would extract higher quality evidence from stimuli, memory, and so on. If IQ were related to boundary separation, a perhaps less likely possibility, people with higher IQ might adjust their decision criteria to require less evidence before making a decision.

To examine these two

Drift rate and the worst performance rule

Table 1 shows results for nine sets of simulated data (1000 subjects per set). For the first three, the across trial variability parameters of the model (η, sz, and st) were set to near 0.0 (0.001). In row 1 of the table, when there was no across subject variability in boundary separation (sa = 0) or the nondecision components (sTer = 0), then drift rate correlated strongly positively with accuracy, and strongly negatively with mean RT and the five RT quantiles (the 0.1, 0.3, 0.5, 0.7, and

Discussion

The results in Table 1, Table 2 show that the diffusion model generates data consistent with the worst performance rule if IQ is correlated with drift rate or if IQ is correlated with boundary separation, but only when other components of processing vary across subjects.

The two possibilities can be discriminated because the correlations between drift rate and data pattern differently than the correlations between boundary separation and data. For drift rate, the correlation with accuracy is

Conclusions

The worst performance rule refers to the empirical finding that when IQ is correlated with RT, the correlation is larger for the slower than the faster responses. The simulations presented in this article show that the diffusion model predicts the worst performance rule if IQ is manifested in drift rate or if it is manifested in boundary separation. The key for the success of the model is variability in the values of components of processing across subjects. The simulations that demonstrated

Acknowledgement

Preparation of this article was supported by NIA grant R01-AG17083 and NIMH grant R37-MH44640. Florian Schmiedek is now at Humboldt-Univeristy, Berlin.

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