One of the assumptions underlying the calculation of almost every d′ in the literature is that the distribution of sensations resulting from repeated presentation of a stimulus is normal and is equal to the distributions produced by the other stimuli in an experiment. This could be a reasonable approximation for pure tones, but it is doubtful whether it applies to more complex stimuli such as speech. A series of magnitude-estimation experiments was carried out, in which subjects were asked to indicate the position of each stimulus on a line on a monitor screen, which ran either from ‘‘soft’’ to ‘‘loud’’ or from /p/ to /t/. The stimuli were practically identical to those used by [L. D. Braida and N. I. Durlach, J. Acoust. Soc. Am. 51, 483–502 (1972), and by M. E. H. Schouten and A. J. van Hessen, J. Acoust. Soc. Am. 92, 1841–1855 (1992)]. Training was done by means of identification of the same stimuli on a similar line, but now subdivided into segments. Each stimulus was presented for magnitude estimation 400 times before and 400 times after training; as a result, the shape and size of each distribution could be traced out.