A new theory of sensory functioning by Laming predicts how the shape of the psychometric function depends on the context in which a signal is presented. The discrimination of intensities of noise was therefore studied with four different stimulus configurations. In one, observers discriminated between two separate noise samples that differed in intensity. In accordance with the theory, a normal probability integral provided a better fit to each observer's data than either of two other functions: a normal integral with respect to the square of the difference, or a normal integral with respect to the fourth power of the difference. In a second task, observers detected an increment in a continuous noise. For eight out of nine sets of data, a square-law function provided a better fit than either a normal integral or fourth-power function. A third task asked observers to decide which of two noises was amplitude modulated. The predicted square-law function provided the best fit for four out of five observers. In a fourth task, one observer detected an interval of amplitude modulation in a continuous noise. As predicted by the theory, a fourth-power function provided the best fit. In addition, Weber fractions for difference discriminations decreased approximately with the square root of sample duration for durations up to 300 msec, whereas Weber fractions for increment detections decreased approximately directly with duration for durations up to 100 msec. The results are usually in qualitative agreement with the theory and often in quantitative agreement as well.