 Behavioural studies provide more evidence. Tests on expert and intermediate level abacus users strongly suggest that MA calculators mentally manipulate an abacus representation so that it passes through the same states that an actual abacus would pass through in solving an addition problem. Without using an actual abacus MA calculators were able to answer correctly questions about intermediates states unique to the abacus-based solution of a problem; moreover, their response times were a monotonic function of the position of the probed state in the sequence of states of the abacus process for solving the problem (Stigler 1984). On top of the ‘intermediate states’ evidence, there is ‘error type’ evidence. Mental addition tests comparing abacus users with American subjects revealed that abacus users made errors of a kind which the Americans did not make, but which were predictable from the distribution of errors in physical abacus addition (Stigler 1984).