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This paper deals with an analysis of psychophysical detection experiments designed to assess the limit of a human observer's level of sensitivity. A mathematical theory of the detection process is introduced that, in contrast to previous theories, provides an analysis of the sequential effects observed in psychophysical data. Two variations of the detection task are considered: information feedback and no-information feedback. In the feedback situation the subject is given information concerning the correctness of his responses, whereas in the no-feedback situation he is not. Data from a visual detection experiment with no-information feedback, and from an auditory detection experiment with information feedback are analyzed in terms of the theory. Finally, some general results are derived concerning the relationship between performance in the feedback situation and the no-feedback situation.