Methods for examining stochastic relationships have been proposed as p
owerful ways to dissociate different underlying psychological processe
s, but a number of problems have undermined conclusions based upon the
se methods. These testing methods and criticisms are reviewed, and the
statistical methods for the testing of stochastic dependence are exam
ined using computer simulation. With each of the methods examined, the
re were difficulties dealing with certain situations that are likely t
o occur in experiments examining dependence between successive tests.
Examination also showed that the sample sizes of some previous studies
were insufficient for findings of moderate amounts of dependence, cal
ling some conclusions of stochastic independence into question. The re
sults of the studies presented here suggest that testing for statistic
al dependence is a statistically perilous technique, but they also sug
gest several ways in which dedicated users of this form of testing can
strengthen its application.