Abstract The analysis of “quasi” grids containing arrays of random numbers was used to explore common interelement distances. Using the Unit of Expected Distance for standardization (Slater, 1976), interelement distances were computed for huge numbers of quasis and the parameters for their distributions specified. The distributions of interelement distances depended on the size of the grids (i.e., the number of constructs). The distances were not symmetrically distributed; there was a marked skewness in distribution. The “significance” of distances (Slater, 1976) should be redefined. The clinical and methodological relevance of the results is demonstrated. Solutions to the statistical problems are suggested.