A significance test for empty corners in scatter diagrams

Regression analysis is usually the statistical tool of choice in hydrologic al studies when there is a strong correlation between two variables. Howeve r, weak correlations can also be of interest if a region within the scatter plot is data-free. This could direct attention to seeking some underlying physical process that might create regions with low probability of generati ng data points. A necessary prior requirement here is to verify that the da ta-free area in the plot is sufficiently large to be a real effect and not a visual illusion. This check can be most simply carried out in a hypothesi s-testing framework. A permutation approach to hypothesis testing is sugges ted for the particular case where a data-free region occupies one of the co rners of a scatter plot, and a test statistic Delta is presented for testin g the statistical significance of the size of this "empty corner". Applicat ion to some rainfall data from southern Israel shows that the new test can sometimes yield higher levels of statistical significance than linear regre ssion when applied to the same data. (C) 1999 Elsevier Science B.V. All rig hts reserved.