The test is based on calculating a design effect for each cluster by
dividing the observed variability by the one expected under independence. The
number of responses and the cluster size are then divided by the design
effect, and a Cochran-Armitage type test statistic is computed based on these
adjusted values.
The implementation aims for testing for increasing trend, and a
one-sided p-value is reported. The test statistic is asymptotically normally
distributed, and a two-sided p-value can be easily computed if needed.