Using performance discontinuities to estimate individual Working-Memory Capacities in serial recall tasks

Although formal models are frequently used to infer working-memory capacity (C) from visual array tasks (Cowan, 2001, Table 2; Luck & Vogel, 2013), Complex Span tasks, on the other hand, are typically scored using variants of the mean number- or the mean proportion of correctly recalled items (e.g. Redick et al, 2012; Conway, 2005). Though useful as indices, they are not interpretable as C, partially because they are confounded by the range of spans presented to the subjects. I propose the "rate change" score of working-memory capacity which has just three parameters: (1) C, the subject's capacity which marks a shift from (2) PC , a high Bernoulli-proportion of correctly recalled items, to (3) Pother, a lower Bernoulli-proportion of recall for further presented items. A Bayesian rate-change model was implemented in JAGS (Plummer, 2003) and applied to data from 46 subjects (25 males) aged 22.4 years (SD = 2.0) who completed a computer-based operation span tasks with four repetitions of spans one through seven, i.e., 28 trials. The population C is 3.7 chunks (95 % CI = 3.2 to 4.2) in line with previous estimates (Cowan, 2001). C constitutes a sharp performance discontinuity between a high rate of recall in working memory (PC = 94.5 %, 95 % credible interval = 93.2 to 96.1 %) and a low rate of recall for items exceeding C (Pother = 9.1 %, CI = 3.9 to 15.0 %). Individual Cs are strongly linearly related to ability as derived from a three-parameter logistic model (r = .987). Classical complex span scores, on the other hand, are non-linearly related to ability. In summary, C is an accurate measure of working-memory ability. Furthermore, the parameters of the rate-change model are theoretically meaningful and robust to the choice of presented spans (e.g., 2-5 vs. 2-7).