Distribution of Magnitude Estimation Judgment Free

Repeated judgments of the loudness of a 1000‐Hz sinusoid were made by a number of observers in various experimental conditions. For all conditions, 20 different stimuli were used spaced 2.5 dB apart in intensity, and 300 to 600 judgments were made at each intensity. In most cases, the mean magnitude estimates were roughly power functions of stimulus intensity with the range of exponents for the individual subjects similar to those reported by earlier investigators. In one experimental condition, without a standard, the ratio of successive responses was compared to the ratio of the intensities of the successive stimuli. The mean ratio of successive responses are roughly power functions of the stimulus intensity ratio of the corresponding signals. The coefficient of variation (m/σ) of these judgments varies markedly as a function of the amount of stimulus change. It is lowest (∼0.1) for the small stimulus changes and reaches an asymptote (∼0.3) if the stimulus changes by 20 dB or more. A theoretical fit to the distribution of these judgments is considered.