Statistical Significance of Clustered Orientation Data on the Sphere: An Empirical Derivation
E. Craig Jowett, Pierre‐Yves F. Robin · The Journal of Geology · 1988
To date there is no statistical theory which assesses the statistical significance of a cluster of data points on a contoured density diagram. In lieu of such a theory, we derive, using a Monte Carlo method, an empirical statistic, P, that can easily yet rigorously test the significance of a cluster of points for a given N at a given level of confidence when counted using a Gaussian weighting function. Multiple random samples of N data points (18 $\leq$ N $\leq$ 800) are drawn from an infinite uniform parent population and counted on the hemisphere to obtain the density surfaces. The empirical point-density statistics $P_{95}$ and $T_{95}$ are the highest and lowest 95th percentiles of the 1000 "peak" and "trough" values calculated for each N. A peak density value (a maximum on a contoured plot) greater than $P_{95}$ for a given N has less than a 5% likelihood of being drawn randomly from a uniform distribution and is therefore a statistically significant cluster at the 95% confidence level. Similarly, a point-density trough less than the derived statistic T for troughs indicates statistical significance. Tables and line graphs of P and T are given as functions of N for seven confidence levels. The statistic $P_{95}$ requires higher point counts than has been previously thought necessary for significance and, moreover, varies substantially with sample size.