Statistical Methods in Medical Research 4ed

Table 10.5 Some of the permutations in the test of equality of standard
deviation: H and L denote the high- and low-protein groups, respectively.
Change in
weight (g)
Permutation
Actual
group 2 3 4 ... 50 388
134 H L H H L
146 H H L H L
104 H H H L L
119 H H H H L
124 H H H H L
161 H H H H L
107 H H H H L
83 H H H H H
113 H H H H H
129 H H H H H
97 H H H H H
123 H H H H H
70 L H H H H
118 L L L L H
101 L L L L H
85 L L L L H
107 L L L L H
132 L L L L H
94 L L L L H
Ratio of
SDs
Monte Carlo tests
10.6Permutation and Monte Carlo tests 295
1 037 1 349 1 116 1 653 ... 0 942
The significance level of a permutation test based on a statistic G is found by
computing G for each of the N permutations allowed under the null hypothesis
and counting the number, M, of these values that are as extreme as, or more
extreme than, the value of G computed from the observed data, Gobs. T he
permutation significance level, Pperm, is then M/N. While conceptually very
attractive, there are often severe practical problems with this approach.
The calculation of the significance level for the permutation test in Example
10.8 required the evaluation of the ratio of standard deviations for 50 388
different permutations. For modern computing machinery this size of task is
relatively straightforward, but if G were more difficult and time-consuming to
evaluate the task could be more daunting. Similarly, if N were larger, the number
of permutations could be substantially greater; even with groups only twice the