as is implied by purely mathematical derivations of the one law from the other. It is, rather, an empirical question whether measurements have been obtained; one which requires justification through the process of stating and testing a well-defined hypothesis in order to ascertain whether specific theoretical criteria for measurement have been satisfied. Some of the relevant criteria were articulated by Thurstone, in a preliminary fashion, including what he termed the additivity criterion. Accordingly, from the point of view of Thurstone's approach, treating the JND as a unit is justifiable provided only that the discriminal dispersions are uniform for all stimuli considered in a given experimental context. Similar issues are associated with Stevens' power law. In addition, Thurstone employed the approach to clarify other similarities and differences between Weber's law, the Weber-Fechner law, and the LCJ. An important clarification is that the LCJ does not necessarily involve a physical stimulus, whereas the other 'laws' do. Another key difference is that Weber's law and the LCJ involve proportions of comparisons in which one stimulus is judged greater than another whereas the so-called Weber-Fechner law does not. The general form The most general form of the LCJ is in which: is the psychological scale value of stimuli i is the sigma corresponding with the proportion of occasions on which the magnitude of stimulus i is judged to exceed the magnitude of stimulus j is the discriminal dispersion of a stimulus is the correlation between the discriminal deviations of stimuli i and j The discriminal dispersion of a stimulus i is the dispersion of fluctuations of the discriminal process for a uniform repeated stimulus, denoted , where represents the mode of such values. Thurstone (1959, p. 20) used the term discriminal process to refer to the "psychological values of psychophysics"; that is, the values on a psychological continuum associated with a given stimulus. Case 5 Thurstone specified five particular cases of the 'law', or measurement model. An important case of the model is Case 5, in which the discriminal dispersions are specified to be uniform and uncorrelated. This form of the model can be represented as follows: where In this case of the model, the difference can be inferred directly from the proportion of instances in which j is judged greater than i if it is hypothesised that is distributed according to some density function, such as the normal distribution or logistic function. In