Encoding of numerical information in memory: Magnitude or nominal?

In studies of long-term memory of multi-digit numbers the leading digit tends to be recalled correctly more often than less significant digits, which has been interpreted as evidence for an analog magnitude encoding of the numbers. However, upon closer examination of data from one of these studies we found that the distribution of recall errors does not fit a model based on analog encoding. Rather, the data suggested an alternative hypothesis that each digit of a number is encoded separately in long-term memory, and that encoding of one or more digits sometimes fails due to insufficient attention in which case they are simply guessed when recall is requested, with no regard for the presented value. To test this hypothesis of nominal encoding with value-independent mistakes, we conducted two studies with a total of 1,080 adults who were asked to recall a single piece of numerical information that had been presented in a story they had read earlier. The information was a three-digit number, manipulated between subjects with respect to its value (between 193 and 975), format (Arabic digits or words), and what it counted (baseball caps or grains of sand). Results were consistent with our hypothesis. Further, the leading digit was recalled correctly more often than less significant digits when the number was presented in Arabic digits but not when the number was presented in words; our interpretation of this finding is that the latter format does not focus readers’ attention on the leading digit.