Monte Carlo procedures

Statistical significance of the subboundary and overlap statistics is evaluated using Monte Carlo procedures, which involve repeatedly recalculating the statistics from randomized data sets. Different randomization methods can be applied, each corresponding to a distinct spatial null model (see Randomization methods).

In general, Monte Carlo Randomization (MCR) procedures follow this sequence:

  1. Following the calculation of statistics from the original data set, observations are randomized according to the chosen null hypothesis.

  2. Boundaries are reestablished for the randomized data, and, if desired, subboundaries are constructed.

  3. Statistics (subboundary or overlap) are recalculated for the new randomized boundaries.

  4. Steps 1-3 are repeated a given number of times, amassing distributions that will be used to calculate p-values for the observed statistics.

  5. The statistics (observed and randomized) are standardized by converting them to Z-scores.

  6. P-values are calculated by comparing the observed statistic to the reference distribution.

See also: