Previously I blogged about an experiment which used the time it takes people to make decisions to try and elucidate something about the underlying mechanisms of information processing (Stafford, Ingram & Gurney, 2011) . This post is about the companion paper to that experiment, reporting some computational modelling inspired by the experiment (Stafford & Gurney, 2011).

The experiment contained a surprising result, or at least a result that I claim should surprise some decision theorists. We has asked people to make a simple judgement – to name out loud the ink colour of a word stimulus, the famous Stroop Task (Stroop, 1935). We found that two factors which affected the decision time had independent effects – the size of the effect of each factors was not effected by the other factor. (The factors were the strength of the colour, in terms of how pale vs deep it was, and how the word was related to the colour, matching it, contradicting it or being irrelevant). This type of result is known as “additive factors” (because they add independently of each other. On a graph of results this looks like parallel lines).

There’s a long tradition in psychology of making an inference from this pattern of experimental results to saying something about the underlying information processing that must be going on. Known as the additive factors methodology (Donders, 1868–1869/1969; Sternberg, 1998), the logic is this: if we systematically vary two things about a decision and they have independent effects on response times, then the two things are operating on separate loci in the decision making architecture – thus proving that there are separate loci in the decision making architecture. Therefore, we can use experiments which measure only outcomes – the time it takes to respond – to ask questions about cognitive architecture; i.e. questions about how information is transformed and combined as it travels between input and output.

The problem with this approach is that it commits a logical fallacy. True separate information processing modules can produce additive factors in response data (A -> B), but that doesn’t mean that additive factors in response time data imply separate information processing modules (B -> A). My work involved taking a widely used model of information processing in the Stroop task (Cohen et al, 1990) and altering it so it contained discrete processing stages, or not. This allowed me to simulate response times in a situation where I knew for certain the architecture – because I’d built the information processing system. The result was surprising. Yes, a system of discrete stages could generate the pattern of data I’d observed experimentally and reported in Stafford, Ingram & Gurney (2011), but so could a single stage system in which all information was continuously processed in parallel, with no discrete information processing modules. Even stranger, both of these kind of systems could be made to produce either additive or non-additive factors without changing their underlying architecture.

The conclusion is straightforward. Although inferring different processing stages (or ‘modules’) from additive factors in data is a venerable tradition in psychology, and one that remains popular (Sternberg, 2011), it is a mistake. As Henson (2011) points out, there’s too much non-linearity in cognitive processing, so that you need additional constraints if you want to make inferences about cognitive modules.

Thanks to Jon Simons for spotting the Sternberg and Henson papers, and so inadvertantly promting this bit of research blogging


Cohen, J. D., Dunbar, K., and McClelland, J. L. (1990). On the control of automatic processes – a parallel distributed-processing account of the Stroop effect. Psychol. Rev. 97, 332–361.

Donders, F. (1868–1869/1969). “Over de snelheid van psychische processen. onderzoekingen gedann in het physiologish laboratorium der utrechtsche hoogeshool,” in Attention and Performance, Vol. II, ed. W. G. Koster (Amsterdam: North-Holland).

Henson, R. N. (2011). How to discover modules in mind and brain: The curse of nonlinearity, and blessing of neuroimaging. A comment on Sternberg (2011). Cognitive Neuropsychology, 28(3-4), 209-223. doi:10.1080/02643294.2011.561305

Stafford, T. and Gurney, K. N.(2011), Additive factors do not imply discrete processing stages: a worked example using models of the Stroop task, Frontiers in Psychology, 2:287.

Stafford, T., Ingram, L., and Gurney, K. N. (2011), Pieron’s Law holds during Stroop conflict: insights into the architecture of decision making, Cognitive Science 35, 1553–1566.

Sternberg, S. (1998). “Discovering mental processing stages: the method of additive factors,” in An Invitation to Cognitive Science: Methods, Models, and Conceptual Issues, 2nd Edn, eds D. Scarborough, and S. Sternberg (Cambridge, MA: MIT Press), 702–863.

Sternberg, S. (2011). Modular processes in mind and brain. Cognitive Neuropsychology, 28(3-4), 156-208. doi:10.1080/02643294.2011.557231

Stroop, J. (1935). Studies of interference in serial verbal reactions. J. Exp. Psychol. 18, 643–662.