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Follow the leader(board) with confidence: Estimating p-values from a single test set with item and response variance

Chris Homan
Lora Aroyo
Shira Wein

Abstract

We tackle the problem of providing accurate, rigorous p-values for comparisons between the results of two evaluated systems whose evaluations are based on a crowdsourced “gold” reference standard. While this problem has been studied before, we argue that the null hypotheses used in previous work have been based on a common fallacy of equality of probabilities, as opposed to the standard null hypothesis that two sets are drawn from the same distribution. We propose using the standard null hypothesis, that two systems’ responses are drawn from the same distribution, and introduce a simulation-based framework for determining the true p-value for this null hypothesis. We explore how to estimate the true p-value from a single test set under different metrics, tests, and sampling methods, and call particular attention to the role of response variance, which exists in crowdsourced annotations as a product of genuine disagreement, and in system predictions as a product of stochastic training regimes, or in generative models as an expected property of the outputs. We find that response variance is a powerful tool for estimating p-values, and present results for the metrics, tests, and sampling methods that make the best p-value estimates in a simple machine learning model comparison

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