Statistical Issues in Reproducibility

Abstract

Reproducibility of quantitative results is a theme that calls for probabilistic models and corresponding statistical methods. This chapter presents the basic notions of statistics. The simplest model is a random sample of normally distributed observations for both the original and the replication data. It will often lead to the conclusion of a failed reproduction because there is stochastic variation between observation campaigns, or unmodeled correlations lead to optimistic measures of precision. Since variation is the critical issue for the assessment of precision, the chapter discusses structures of variation. It explains the regression models and their use for reproducibility assessment. The chapter covers the issue of model development and consequences for reproducibility, addresses issues of the analysis of large datasets and comments on Bayesian statistics and reproducibility. The general rule by which updating is performed is the formula of Bayes connecting conditional probabilities-whence the name of the paradigm.

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