The cost of errors: confusion analysis and the mental representation of familiar and unfamiliar digits
People express quantities using a remarkably small set of units – digits. Confusing digits could be costly, and not all confusions are equal; confusing a price tag of 2 dollars with 9 dollars is naturally more costly than confusing 2 with 3. Confusion patterns are intimately related to the distances between mental representations, which are hypothetical internal symbols said to stand for, or represent, ‘real’ external stimuli. The distance between the mental representations of two digits could be determined by their numerical distance. Alternatively, it could be driven by visual similarity. In an English speaking cohort, we investigated the mental representations of familiar and unfamiliar numbers (4 sets: Arabic, Chinese, Thai, and non-symbolic dots) through a set of identification experiments, using multi-dimensional scaling and cluster analysis. We controlled for undesired effects of response bias using Luce’s choice model. Our findings show Arabic, Chinese and Thai numerals were represented in the mental space by perceptual similarities. We also find non-symbolic dots were represented by perceptual and numerical similarities. This work is a novel contribution to the literature and lays the foundation for further investigations into the mental representation of numerals across cultures.