Unbiased Low-Variance Estimators for Precision and Related Information Retrieval Effectiveness Measures

This work describes an estimator from which unbiased measurements of precision, rank-biased precision, and cumulative gain may be derived from a uniform or non-uniform sample of relevance assessments. Adversarial testing supports the theory that our estimator yields unbiased low-variance measurements from sparse samples, even when used to measure results that are qualitatively different from those returned by known information retrieval methods. Our results suggest that test collections using sampling to select documents for relevance assessment yield more accurate measurements than test collections using pooling, especially for the results of retrieval methods not contributing to the pool.