Attending to one stimulus and not another usually improves judgments of the attended stimulus. By the "noise reduction hypothesis", this improvement is due to excluding information from irrelevant stimuli rather than improving the processing of the relevant stimulus. In this talk, I briefly review my prior work on the noise reduction hypothesis in accuracy experiments. Then I present new work on attention in response time experiments. The analysis depends on the development of a quantitative decision theory for response time. Both the decision and attention aspects of the theory are tested in behavioral experiments. I also describe research on the neural basis of the decision theory. In conclusion, I argue that noise reduction is the primary attentional mechanism for simple perceptual tasks.