On the measurement of test collection reliability

The reliability of a test collection is proportional to the number of queries it contains. But building a collection with many queries is expensive, so researchers have to find a balance between reliability and cost. Previous work on the measurement of test collection reliability relied on data-based approaches that contemplated random what if scenarios, and provided indicators such as swap rates and Kendall tau correlations. Generalizability Theory was proposed as an alternative founded on analysis of variance that provides reliability indicators based on statistical theory. However, these reliability indicators are hard to interpret in practice, because they do not correspond to well known indicators like Kendall tau correlation. We empirically established these relationships based on data from over 40 TREC collections, thus filling the gap in the practical interpretation of Generalizability Theory. We also review the computation of these indicators, and show that they are extremely dependent on the sample of systems and queries used, so much that the required number of queries to achieve a certain level of reliability can vary in orders of magnitude. We discuss the computation of confidence intervals for these statistics, providing a much more reliable tool to measure test collection reliability. Reflecting upon all these results, we review a wealth of TREC test collections, arguing that they are possibly not as reliable as generally accepted and that the common choice of 50 queries is insufficient even for stable rankings.