The method of successive intervals, developed as an extension of Thurstone's scaling approach, asks observers to sort stimuli into ordered categories. By treating category boundaries as points on an underlying normal distribution, the method recovers interval-scale values for both the stimuli and the category boundaries.
Procedure and Analysis
Observers assign each stimulus to one of k ordered categories. The cumulative proportions at each category boundary are converted to z-scores using the inverse normal distribution. Under the assumption that the discriminal processes are normally distributed with equal variance, these z-scores define category boundaries on the psychological continuum. Stimulus scale values are estimated from the mean or median of their distribution across categories.
z_ig = Φ⁻¹(P_ig)
Scale value sᵢ = mean of boundary values weighted by frequency
Relationship to Other Methods
Successive intervals is closely related to Thurstone's method of equal-appearing intervals, which assumes that observers can maintain equally spaced category boundaries. The successive intervals method relaxes this assumption, allowing boundaries to be estimated from the data. It occupies a middle ground between paired comparisons (which use only ordinal judgments but require many trials) and direct rating (which assumes interval properties of the response scale).
The method has been widely used in attitude measurement, psychophysical scaling, and quality assessment where stimuli are too numerous for full paired comparison designs.