Empirical formula for creating error bars for the method of paired comparison
Abstract
The method of paired comparison based on Thurstone’s
case V of his law of comparative judgments is often used as a psychophysical
method to derive interval scales of perceptual qualities
in imaging applications. However, methods for determining confi-
dence intervals and critical distances for significant differences have
been elusive, leading some to abandon the simple analysis provided
by Thurstone’s formulation. Monte Carlo simulations of paired comparison
experiments were performed in order to derive an empirical
formula for determining error. The results show that the variation in
the distribution of experimental results can be well predicted as a
function of stimulus number and the number of observations. Using
these results, confidence intervals and critical values for comparisons
can be made using traditional statistical methods.