There are two alternative hypotheses in overlap statistics, either boundary association or boundary avoidance. For two sets of boundaries, G and H, boundaries that overlap would have high values of OS and low values of OG, OH, and OGH. Low values of OS and high values of OG, OH, and OGH indicate boundary avoidance.
The table below provides a quick reference:
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You can use Monte Carlo randomization to determine whether the observed value of a test statistic is either significantly high or significantly low. BoundarySeer will present the p-values for the upper and lower tails of the Monte Carlo distribution. Use the table above to determine which tail to evaluate for which alternative hypothesis. To evaluate whether a test statistic is unusually low, examine the lower tail p-value (from the lower end of the distribution). To evaluate whether a test statistic is unusually high, examine the upper tail p-value (from the upper end of the distribution). (See also: Calculating Monte Carlo p-values)
Simulation studies (Jacquez 1995) demonstrated that the significance of OS is related to the presence of large-scale boundaries (boundaries whose lengths are on the same scale as sampling), even when H is dependent on G. OG is significant when boundaries for G are nearer to boundaries for H than expected, and a similar interpretation follows for OH. OGH measures the simultaneous fit between the two boundary sets.
BE CAREFUL interpreting OS, because there are many situations where the spatial support for the two boundaries preclude any direct overlap. If this happens, OS will always be zero, and it should not be included in the analysis.
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