A Simple Approximation For Random Rankings Stress Values

Potentially more convenient than either a table or a graph of random rankings stress values is a simple analytic expression which takes as arguments N, the number of points, and D, the number of dimensions and then yields the expected stress value. Such a function is developed here, and it is shown that the error of the approximation is of the same magnitude as the standard error of the means of the original Monte Carlo data. The approximation is highly accurate for 10 < N < 60 and 1 < D < 5. The present paper represents an extension of Spence and Ogilvie (1973).