Abstract: We measure how accurately replication of experimental results can be predicted by black-box statistical models. With data from four large-scale replication projects in experimental psychology and economics, and techniques from machine learning, we train predictive models and study which variables drive predictable replication. The models predicts binary replication with a cross-validated accuracy rate of 70% (AUC of 0.77) and estimates of relative effect sizes with a Spearman ρ of 0.38. The accuracy level is similar to market-aggregated beliefs of peer scientists [1, 2]. The predictive power is validated in a pre-registered out of sample test of the outcome of [3], where 71% (AUC of 0.73) of replications are predicted correctly and effect size correlations amount to ρ = 0.25. Basic features such as the sample and effect sizes in original papers, and whether reported effects are single-variable main effects or two-variable interactions, are predictive of successful replication. The models presented in this paper are simple tools to produce cheap, prognostic replicability metrics. These models could be useful in institutionalizing the process of evaluation of new findings and guiding resources to those direct replications that are likely to be most informative.
1 Introduction
Replication lies at the heart of the process by which science accumulates knowledge. The ability of other scientists to replicate an experiment or analysis demonstrates robustness, guards against false positives, puts an appropriate burden on scientists to make replication easy for others to do, and can expose the various “researcher degrees of freedom” like p-hacking or forking [4–20].
The most basic type of replication is “direct” replication, which strives to reproduce the creation or analysis of data using methods as close to those used in the original science as possible [21].
Direct replication is difficult and sometimes thankless. It requires the original scientists to be crystal clear about details of their scientific protocol, often demanding extra effort years later. Conducting a replication of other scientists’ work takes time and money, and often has less professional reward than original discovery.
Because direct replication requires scarce scientific resources, it is useful to have methods to evaluate which original findings are likely to replicate robustly or not. Moreover, implicit subjective judgments about replicability are made during many types of science evaluations. Replicability beliefs can be influential when giving advice to granting agencies and foundations on what research deserves funding, when reviewing articles which have been submitted to peer-reviewed journals, during hiring and promotion of colleagues, and in a wide range of informal “post-publication review” processes, whether at large international conferences or small kaffeeklatches.
The process of examining and possibly replicating research is long and complicated. For example, the publication of [22] resulted in a series of replications and subsequent replies [23–26]. The original findings were scrutinized in a thorough and long process that yielded a better understanding of the results and their limitations. Many more published findings would benefit from such examination. The community is in dire need of tools that can make this work more efficient. Statcheck [27] is one such framework that can automatically identify statistical errors in finished papers. In the same vein, we present here a new tool to automatically evaluate the replicability of laboratory experiments in the social sciences.
There are many potential ways to assess whether results will replicate. We propose a simple, black-box, statistical approach, which is deliberately automated in order to require little subjective peer judgment and to minimize costs. This approach leverages the hard work of several recent multi-investigator teams who performed direct replications of experiments in psychology and economics [2, 7, 28, 29]. Based on these actual replications, we fit statistical models to predict replication and analyze which objective features of studies are associated with replicability.
We have 131 direct replications in our dataset. Each can be judged categorically by whether it replicated or not, by a pre-announced binary statistical criterion. The degree of replication can also be judged on a continuous numerical scale, by the size of the effect estimated in the replication compared to the size of the effect in the original study. As binary criterion, we call replications with significant (p ≤ 0.05) effects in the same direction as the original study successful. For the continuous measure, we study the ratio of effect sizes, standardized to correlation coefficients. Our method uses machine learning to predict outcomes and identify the characteristics of study-replication pairs that can best explain the observed replication results [30–33].
We divide the objective features of the original experiment into two classes. The first contains the statistical design properties and outcomes: among these features we have sample size, the effect size and p-value originally measured, and whether a finding is an effect of one variable or an interaction between multiple variables. The second class is the descriptive aspects of the original study which go beyond statistics: these features include how often a published paper has been cited and the number and past success of authors, but also how subjects were compensated. Furthermore, since our model is designed to predict the outcome of specific replication attempts we also include similar properties about the replication that were known beforehand. We also include variables that characterize the difference between the original and replication experiments—such as whether they were conducted in the same country or used the same pool of subjects. See S1 Table for a complete list of variables, and S2 Table for summary statistics.
The statistical and descriptive features are objective. In addition, for a sample of 55 of the study-replication pairs we also have measures of subjective beliefs of peer scientists about how likely a replication attempt was to result in a categorical Yes/No replication, on a 0-100% scale, based on survey responses and prediction market prices [1, 2]. Market participants in these studies predicted replication with an accuracy of 65.5% (assuming that market prices reflect replication probabilities [34] and using a decision threshold of 0.5).
Our proposed model should be seen as a proof-of-concept. It is fitted on an arguably too small data set with an indiscriminately selected feature set. Still, its performance is on par with the predictions of professionals, hinting at a promising future for the use of statistical tools in the evaluation of replicability.
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