Variability of magnitude estimates: A timing theory analysis

Three procedures for magnitude estimation were investigated, and a sufficient number of responses were obtained to make reasonable estimates of both the mean and variance of the responses. The conventional magnitude estimate procedure, without a standard signal, appeared to produce the most sensible data. The best method of establishing the central tendency of the data appears to be the plot of the mean ratio of successive responses against the intensity ratio of the corresponding signal intensities. When this is done, the average response ratio increases roughly as a power function of the signal ratios. The coefficient of variation, σ/m, varies from about 0.1 for small signal ratios and increases to 0.3 at about 20 dB and greater signal separations. The distribution of response ratios appears to be reasonably well approximated by a beta distribution. The change in σ/m with signal ratio is suggestive of an attention mechanism in which the sample size depends on the location of the attention band. The ratio estimation procedure suffers badly from discrete number tendencies.