A subboundary is a set of connected Boundary Elements (BEs). The set of subboundaries found for a data set or data sets make up the boundary. There are two alternative hypotheses in subboundary statistics, either large-scale boundaries or boundary fragmentation .
Under a boundary-generating process, we would expect a contiguous boundary with few subboundaries (Ns), few singletons (N1), high subboundary length (L, both mean and max), high subboundary diameter (D, both mean and max), and low subboundary branchiness (diameter to length ratio, D/L).
Under boundary fragmentation, we would expect lots of singleton subboundaries (high Ns and N1), low subboundary length, low diameter, and high branchiness.
The following table summarizes the predictions of each alternative hypothesis.
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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 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).
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