Anchoring bias in mental arithmetic

Mental arithmetic is widely studied, both with symbolic digits and with non-symbolic dot patterns that require operand estimation. Several studies reported surprising biases in adults' performance with both formats while their direction (over/underestimation in addition/subtraction) remains controversial (operational momentum effect or OM; Prado & Knops, Prado and Knops, Psychonomic Bulletin & Review, in Press., 2024). Theoretical accounts of OM make opposing predictions, thus enabling a decisive test: Using symbolic stimuli and responses, we enabled accurate operand encoding and result reporting, thus leaving mental calculation as only source of bias. Importantly, we manipulated operand order through calculation instructions (e.g., "29 + 19" vs. "add 19 to 29") to assess the crucial role of first operand size as cognitive anchor. With both auditory (Experiment 1, N = 30) and visual presentation (Experiment 2, N = 30), we observed reverse OM, i.e., overestimations in subtraction and underestimations in addition. Importantly, this instance of operation-based anchoring was independent of a second anchoring effect related to operand order: A large operand is a stronger anchor when mentioned first. Our discovery of both operation-based and order-based anchoring extends the well-known anchoring effect into mental arithmetic and eliminates several competing theories about the origin of OM.