Message Repetition and Receiver Confirmation of Messages in Noise

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Abstract
A receiver may be required to decide whether the message he has recorded is or is not the message actually received. The degree of certainty needed for confirmation (the criterion) may be controlled by instructions. A sequence of decisions is generated by repeatedly sending each of a set of messages until the set is confirmed. A simple stochastic model assumes that the probability of confirmation, py, is constant over such a sequence. If N messages are sent, the expected number confirmed after the first n presentations is E(n) = N[1 − (1 − py)n]. Two experimental tests were (1) of the constancy of py by noting whether the equation for E(n) holds, and (2) of the constancy of py's three component probabilities: the probabilities of correct reception, correct confirmation, and incorrect confirmation. Receivers listened under two noise conditions to sets of several hundred messages each. Each message was immediately repeated until confirmed. Estimates of py and of the component probabilities were made from proportions of correct and incorrect responses. The data show that the assumption of constant py yields a very accurate description of the process, and justify the more basic assumption that py's three components are constant over repeated trials. Further, the data are in excellent agreement with predictions from the theory of the total number of communication events required before the entire set of N messages is confirmed, and of the total numbers of correct and incorrect confirmations.

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