Measures and tests of alignment

Abstract

SUMMARY Approaches to the question of the alignment of objects in a two-dimensional region via correlation, maximum likelihood test and procrustean distance lead to equivalent versions of the ellipticity statistic, L. The distribution of L in the Gaussian and uniform cases is discussed. This paper considers the problem of measuring the degree of alignment of objects spatially located in some two-dimensional region and of assessing the statistical significance of near alignment. Broadbent (1980) and Kendall & Kendall (1980) discuss the detection of the intentional alignment of megalithic sites and Zuiderwijk (1982) discusses whether a group of quasars exhibit a surprising degree of alignment. Many measures of alignment can be suggested; we review briefly the angular and width criteria used in the above papers. The main concern of this paper is the L statistic introduced in the next section.