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Background  Testing for clustering at multiple ranges within a single dataset is a common practice in spatial epidemiology. It is not documented whether this approach has an impact on the type 1 error rate.    Methods  We estimated the family-wise error rate (FWE) for the difference in Ripley’s  K  functions test, when testing at an increasing number of ranges at an alpha-level of 0.05. Case and control locations were generated from a Cox process on a square area the size of the continental US (≈3,000,000 mi 2 ). Two thousand Monte Carlo replicates were used to estimate the FWE with 95% confidence intervals when testing for clustering at one range, as well as 10, 50, and 100 equidistant ranges.    Results  The estimated FWE and 95% confidence intervals when testing 10, 50, and 100 ranges were 0.22 (0.20 - 0.24), 0.34 (0.31 - 0.36), and 0.36 (0.34 - 0.38), respectively.    Conclusions  Testing for clustering at multiple ranges within a single dataset inflated the FWE above the nominal level of 0.05. Investigators should construct simultaneous critical envelopes (available in spatstat package in R), or use a test statistic that integrates the test statistics from each range, as suggested by the creators of the difference in Ripley’s  K  functions test.

Testing for clustering at many ranges inflates family-wise error rate (FWE)