Some Speed, Error and Difficulty Relationships within a Problem-solving Situation

Abstract

DURING the past three years, experiments have been conducted with subjects who have been given the task of solving mental-test items of a particular type¹ (Thurstone ‘letter-series’ items). Suppose P_C be the probability that a particular subject will continue to work at a particular problem for some time t before giving it up, and let P_E be the probability that if a solution is recorded within this time it will be the correct one. If the universe of discourse is now restricted to correctly solved items, the probability (P_S) that a particular correct solution will be returned within a period of t sec. after the moment the problem is presented will be a function both of the dynamics of the problem-solving process as such and also of P_C, for if P_C ≠ 1 at time t then P_S must be modified, and if P_C = 0, P_S must be zero also. Let P_S be defined as the probability which would obtain if P_C = 1 for t = ∞. No comprehensive statement can be made about a person's ability to solve a problem which does not involve at least these three probabilities, that is, any attempt to measure ‘intelligence’ by mental-test methods should involve assessments of P_C, P_E and P_S.