About subboundary statistics

Subboundary statistics evaluate subboundary contiguity for difference boundaries. The fundamental question is whether the connections between boundary elements are statistically unusual, or whether their strength could be explained by chance. The statistics themselves were drawn from planar graph theory by Oden et al. (1993).

This method analyzes subboundaries to determine whether they possess significant characteristics, such as length, branchiness, and diameter. Whether the statistics are unusual is evaluated with Monte Carlo procedures.

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 two alternative hypotheses (Ha).

Hypotheses

Ho-CSR	Boundaries occur by chance; the values of observations at nearby candidate boundary elements are distributed according to complete spatial randomness. Thus they are not particularly contiguous, with intermediate values of the test statistics.
Ho-SA	Boundaries occur because of spatial autocorrelation; the values of observations at nearby candidate boundary elements are correlated. Thus, subboundary connections are short, with intermediate values of the test statistics.
Ha1	Large-scale boundaries exist, the values of the test statistics will show high boundary contiguity.
Ha2	Boundaries are fragmented, the values of the test statistics will show lower contiguity than expected by chance.

See also:

Tutorial examples: