Statistics of free memory recall

Numerous studies analyzed the performance of participants in free recall of randomly assembled lists of words with the focus on the average number of words recalled for different experimental parameters such as list length, presentation speed, etc. The distribution of performance around the mean was not systematically studied, even though it is well-known that recall is an unpredictable process resulting in highly variable results over different trials. We recently introduced the mathematical model of free recall that reproduced well the average performance of human participants in experiments with randomly assembled lists of words or short sentences. The model assumes that during recall, each memory item currently recalled triggers a recall of a next item based on the random symmetric matrix of similarity measures between items in the list. When applying the model to experimental data, a crucial assumption was made that upon presentation, a certain fraction of presented items remain in memory that are candidates for recall, and that the number of such items can be estimated with recognition experiments performed by the same group of participants under identical conditions of item presentation as in the recall experiments. It is not clear whether this assumption is valid under different experimental paradigms and with different groups of participants. Here we propose that calculating the variance of recall performance allows one to formulate interesting predictions that can be tested without performing recognition experiments. Comparison of model predictions with experimental data on young and old participants indicates that the same recall algorithm is involved in both groups, even though old participants may have fewer candidate memory items for recall after presentation.