  Statistical significance testing is widely accepted as a means to assess how
well a difference in effectiveness reflects an actual difference between
systems, as opposed to random noise because of the selection of topics.
According to recent surveys on SIGIR, CIKM, ECIR and TOIS papers, the t-test is
the most popular choice among IR researchers. However, previous work has
suggested computer intensive tests like the bootstrap or the permutation test,
based mainly on theoretical arguments. On empirical grounds, others have
suggested non-parametric alternatives such as the Wilcoxon test. Indeed, the
question of which tests we should use has accompanied IR and related fields for
decades now. Previous theoretical studies on this matter were limited in that
we know that test assumptions are not met in IR experiments, and empirical
studies were limited in that we do not have the necessary control over the null
hypotheses to compute actual Type I and Type II error rates under realistic
conditions. Therefore, not only is it unclear which test to use, but also how
much trust we should put in them. In contrast to past studies, in this paper we
employ a recent simulation methodology from TREC data to go around these
limitations. Our study comprises over 500 million p-values computed for a range
of tests, systems, effectiveness measures, topic set sizes and effect sizes,
and for both the 2-tail and 1-tail cases. Having such a large supply of IR
evaluation data with full knowledge of the null hypotheses, we are finally in a
position to evaluate how well statistical significance tests really behave with
IR data, and make sound recommendations for practitioners.
