Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations
Table 6
Presented are the means (±SD (standard deviations)) of the off-diagonal entries, , , and their difference and the rejection rate estimates under Case I patterns in (33) with , at (a) and rejection rate estimates based on Monte Carlo randomization with and 1000 Monte Carlo randomization steps are performed for each of generated samples under Case I patterns (b). and stand for the empirical rejection rate estimates for Pielou's first type of symmetry test using approximation with and without Yates' continuity correction, respectively; stands for the exact binomial version of Pielou's first type of symmetry test conditional on ; stands for Dixon's symmetry test; is for Pielou's second type of symmetry test; stands for the exact test on the -symmetry contingency table.
(a)
Mean ± SD
Rejection rate estimates for Case I patterns
I-(i)
.0018
.0060
.0721
.0092
.0379
.0359
I-(ii)
.0118
.0511
.3109
.0017
.0345
.0324
I-(iii)
.0338
.0919
.5345
.0002
.0324
.0296
(b)
Rejection rate estimates for Case I patterns based on Monte Carlo randomization