  An association rule is statistically significant, if it has a small
probability to occur by chance. It is well-known that the traditional
frequency-confidence framework does not produce statistically significant
rules. It can both accept spurious rules (type 1 error) and reject significant
rules (type 2 error). The same problem concerns other commonly used
interestingness measures and pruning heuristics.
  In this paper, we inspect the most common measure functions - frequency,
confidence, degree of dependence, $\chi^2$, correlation coefficient, and
$J$-measure - and redundancy reduction techniques. For each technique, we
analyze whether it can make type 1 or type 2 error and the conditions under
which the error occurs. In addition, we give new theoretical results which can
be use to guide the search for statistically significant association rules.
