Ratio scale measurement of the perceived lengths of lines

In Experiments 1 and 2, magnitude and category estimates of perceived line length difference were used to rank order 36 pairs of lines with respect to the psychological length difference between the lines forming a pair. In Experiment 3 magnitude estimates of line length ratios were used to order the same 36 pairs with respect to the psychological length ratio between the lines comprising a pair. A nonmetric analysis of the rank-order of the difference and ratio judgments was used to construct a ratio scale of perceived line length. Perceived line length was found to be a power function of physical line length with an exponent of .46. In Experiments 4 and 5, magnitude and category estimates of line length similarity were obtained. A nonmetric analysis of these data indicated that similarity judgments were monotonic inverses of judgments of psychological ratios.