Research Article

Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations

Table 5

The empirical significance levels of the tests under RL Cases  1–3 with for each of 100 background realization at . The empirical size labeling is as in Table 3. stands for the empirical size estimates of the exact tests for Pielou's second type of symmetry (the table exclusive version).

RL Case  1

10 .00011 .00089 .00092 .04368 .04989 .04205
20 .00018 .00096 .00106 .04797 .05283 .04831
30 .00017 .00095 .00110 .05037 .05147 .04974
40 .00016 .00056 .00042 .05156 .05242 .04994
50 .00028 .00070 .00050 .04981 .05020 .04934

RL Case  2

20 .00016 .00089 .00109 .04907 .05298 .04987
30 .00016 .00090 .00063 .05087 .05143 .05258
40 .00015 .00069 .00048 .04880 .05087 .05222
50 .00026 .00099 .00079 .04700 .05010 .05271
60 .00027 .00097 .00084 .04991 .04985 .05104

RL Case  3

2 .00018 .00063 .00065 .05158 .05241 .05006
4 .00023 .08451 .00083 .04848 .05024 .04988
6 .00012 .00051 .00048 .04953 .05061 .05057
8 .00024 .00076 .00074 .05075 .05007 .04963
10 .00024 .00070 .00083 .04939 .05087 .05063