Variations of the triangular method and the relationship of its unidimensional probabilistic models to three‐alternative forced‐choice signal detection theory models

The experimental procedure involved in the application of the statistical triangle test and some of the limitations of this method are briefly discussed. Two types of unidimensional distance models, the triangle constant method and the normal Thurstone‐Ura model, are briefly reviewed and the logistic Thurstone‐Ura model is developed. The two versions of the Thurstone‐Ura model are shown to be remarkably different from the corresponding versions of the three‐alternative forced‐choice signal detection theory model. Some theoretical and experimental differences between the triangular constant method model, the Thurstone‐Ura model and the 3‐AFC SDT model are discussed. Finally, by analysis of experimental data, it is shown that the theoretical distinction between the Thurstone‐Ura model and the 3‐AFC SDT model is useful because it appeared the key for the resolution of the ‘paradox of discriminatory non‐discriminators' (Gridgeman, 1970).