Overlap statistics examine whether boundaries for two or more variables coincide, or overlap, to a significant extent. BoundarySeer implements methods developed for difference boundaries by Jacquez (1995).
The exact form of the null hypothesis (Ho) depends on the null spatial model. You choose the null spatial model when you specify the randomization procedure. There are two null hypotheses (CSR and SA), and three alternative hypotheses (Ha).
Hypotheses
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Ho-CSR |
Boundaries are distributed according to complete spatial randomness. Boundary overlap will occur randomly. |
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Ho-SA |
The values of observations at nearby boundary elements are correlated. Boundary overlap may occur on a local scale, but not on a large scale. Boundary overlap statistics will be intermediate. |
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Ha1 |
The two sets of boundaries coincide. There is large scale overlap between boundaries. |
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Ha2 |
Overlap is directional: one set of boundaries depends on another set of boundaries. |
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Ha3 |
The boundaries avoid each other, boundaries will overlap less than expected by chance. |
Your alternative hypothesis will determine how you randomize the data set. If you think that one set of boundaries depends on another, randomize the data set of the boundary you think may be dependent. For example, if you are testing the hypothesis that the distribution of a plant ecotone is a response to boundaries in soil types, randomize the plant boundaries set when you do an overlap analysis. If you think that two boundaries are associated with each other, randomize both.
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