Towards Meaningful Statements in IR Evaluation. Mapping Evaluation Measures to Interval Scales

Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and to what extent these findings apply to actual evaluations and this opened a debate in the community with researchers standing on opposite positions about whether this should be considered an issue (or not) and to what extent. In this paper, we first give an introduction to the representational measurement theory explaining why certain operations and significance tests are permissible only with scales of a certain level. For that, we introduce the notion of meaningfulness specifying the conditions under which the truth (or falsity) of a statement is invariant under permissible transformations of a scale. Furthermore, we show how the recall base and the length of the run may make comparison and aggregation across topics problematic. Then we propose a straightforward and powerful approach for turning an evaluation measure into an interval scale, and describe an experimental evaluation of the differences between using the original measures and the interval-scaled ones. For all the regarded measures - namely Precision, Recall, Average Precision, (Normalized) Discounted Cumulative Gain, Rank-Biased Precision and Reciprocal Rank - we observe substantial effects, both on the order of average values and on the outcome of significance tests. For the latter, previously significant differences turn out to be insignificant, while insignificant ones become significant. The effect varies remarkably between the tests considered but overall, on average, we observed a 25% change in the decision about which systems are significantly different and which are not.