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Some aspects of the quantitative interpretation of stress are discussed on the basis of random sets of synthetic dissimilarity matrices. In Section 1 the relation between measurement error and stress is studied. Synthetic dissimilarities are obtained starting from a random configuration of n points ( n = 8, 10, and 12) in t dimensions (1 ≤ t ≤ 3), and adding a fractional error to the interpoint distances. These dissimilarity sets are then analysed in m dimensions (1 ≤ m ≤ 5). The results give an idea of how the stress is influenced by measurement error and the chosen dimensionality of the analysis. In practice, the results can be used for estimating both the true dimensionality and the measurement error of a set of data. In Section 2 the probability distribution of the stress‐percentages in m dimensions (1 ≤ m ≤ 5) is estimated in cases of randomly chosen dissimilarities among n points (7 ≤ n ≤ 12). The results can be an aid in determining the significance of a multidimensional representation of experimental data.
Wagenaar et al. (Sat,) studied this question.