Integrated diffusion models for distance effects in number memory

I evaluated three models for the representation of numbers in memory. These were integrated with the diffusion decision model to explain accuracy and response time (RT) data from a recognition memory experiment in which the stimuli were two-digit numbers. The integrated models accounted for distance/confusability effects: when a test number was numerically close to a studied number, accuracy was lower and RTs were longer than when a test number was numerically far from a studied number. For two of the models, the representations of numbers are distributed over number (with Gaussian or exponential distributions) and the overlap between the distributions of a studied number and a test number provides the evidence (drift rate) on which a decision is made. For the third, the exponential gradient model, drift rate is an exponential function of the numerical distance between studied and test numbers. The exponential gradient model fit the data slightly better than the two overlap models. Monte Carlo simulations showed that the variability in the important parameter estimates from fitting data collected over 30–40 min is smaller than the variability among individuals, allowing differences among individuals to be studied. A second experiment compared number memory and number discrimination tasks and results showed different distance effects. Number memory had an exponential-like distance-effect and number discrimination had a linear function which shows radically different representations drive the two tasks.