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While there has been significant research on statistical techniques for comparing two information retrieval (IR) systems, many IR experiments test more than two systems. This can lead to inflated false discoveries due to the multiple-comparison problem (MCP). A few IR studies have investigated multiple comparison procedures; these studies mostly use TREC data and control the familywise error rate. In this study, we extend their investigation to include recommendation system evaluation data as well as multiple comparison procedures that controls for False Discovery Rate (FDR). 

The strategy for selecting candidate sets — the set of items that the recommendation system is expected to rank for each user — is an important decision in carrying out an offline top-N recommender system evaluation. The set of candidates is composed of the union of the user’s test items and an arbitrary number of non-relevant items that we refer to as decoys. Previous studies have aimed to understand the effect of different candidate set sizes and selection strategies on evaluation. In this paper, we extend this knowledge by studying the specific interaction of candidate set selection strategies with popularity bias, and use simulation to assess whether sampled candidate sets result in metric estimates that are less biased with respect to the true metric values under complete data that is typically unavailable in ordinary experiments. 

A number of information retrieval studies have been done to assess which statistical techniques are appropriate for comparing systems. However, these studies are focused on TREC-style experiments, which typically have fewer than 100 topics. There is no similar line of work for large search and recommendation experiments; such studies typically have thousands of topics or users and much sparser relevance judgements, so it is not clear if recommendations for analyzing traditional TREC experiments apply to these settings. In this paper, we empirically study the behavior of significance tests with large search and recommendation evaluation data. Our results show that the Wilcoxon and Sign tests show significantly higher Type-1 error rates for large sample sizes than the bootstrap, randomization and t-tests, which were more consistent with the expected error rate. While the statistical tests displayed differences in their power for smaller sample sizes, they showed no difference in their power for large sample sizes. We recommend the sign and Wilcoxon tests should not be used to analyze large scale evaluation results. Our result demonstrate that with Top-\(N\) recommendation and large search evaluation data, most tests would have a 100% chance of finding statistically significant results. Therefore, the effect size should be used to determine practical or scientific significance.