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De Santis F, Gubbiotti S. On the distribution of the power function for the scale parameter of exponential families. Stat Med 2024; 43:1973-1992. [PMID: 38634314 DOI: 10.1002/sim.10043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Revised: 01/17/2024] [Accepted: 02/09/2024] [Indexed: 04/19/2024]
Abstract
The expected value of the standard power function of a test, computed with respect to a design prior distribution, is often used to evaluate the probability of success of an experiment. However, looking only at the expected value might be reductive. Instead, the whole probability distribution of the power function induced by the design prior can be exploited. In this article we consider one-sided testing for the scale parameter of exponential families and we derive general unifying expressions for cumulative distribution and density functions of the random power. Sample size determination criteria based on alternative summaries of these functions are discussed. The study sheds light on the relevance of the choice of the design prior in order to construct a successful experiment.
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Affiliation(s)
- Fulvio De Santis
- Dipartimento di Scienze Statistiche, Sapienza University of Rome, Rome, Italy
| | - Stefania Gubbiotti
- Dipartimento di Scienze Statistiche, Sapienza University of Rome, Rome, Italy
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2
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Liu CC, Yu RX. Epistemic uncertainty in Bayesian predictive probabilities. J Biopharm Stat 2024; 34:394-412. [PMID: 37157818 DOI: 10.1080/10543406.2023.2204943] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Accepted: 04/15/2023] [Indexed: 05/10/2023]
Abstract
Bayesian predictive probabilities have become a ubiquitous tool for design and monitoring of clinical trials. The typical procedure is to average predictive probabilities over the prior or posterior distributions. In this paper, we highlight the limitations of relying solely on averaging, and propose the reporting of intervals or quantiles for the predictive probabilities. These intervals formalize the intuition that uncertainty decreases with more information. We present four different applications (Phase 1 dose escalation, early stopping for futility, sample size re-estimation, and assurance/probability of success) to demonstrate the practicality and generality of the proposed approach.
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Affiliation(s)
- Charles C Liu
- Department of Biostatistics, Gilead Sciences, Foster City, CA, USA
| | - Ron Xiaolong Yu
- Department of Biostatistics, Gilead Sciences, Foster City, CA, USA
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3
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Liu Q, Hu G, Ye B, Wang S, Wu Y. Sample size re-estimation in Phase 2 dose-finding: Conditional power versus Bayesian predictive power. Pharm Stat 2023; 22:349-364. [PMID: 36418025 DOI: 10.1002/pst.2275] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2019] [Revised: 08/31/2022] [Accepted: 11/07/2022] [Indexed: 11/25/2022]
Abstract
Unblinded sample size re-estimation (SSR) is often planned in a clinical trial when there is large uncertainty about the true treatment effect. For Proof-of Concept (PoC) in a Phase II dose finding study, contrast test can be adopted to leverage information from all treatment groups. In this article, we propose two-stage SSR designs using frequentist conditional power (CP) and Bayesian predictive power (PP) for both single and multiple contrast tests. The Bayesian SSR can be implemented under a wide range of prior settings to incorporate different prior knowledge. Taking the adaptivity into account, all type I errors of final analysis in this paper are rigorously protected. Simulation studies are carried out to demonstrate the advantages of unblinded SSR in multi-arm trials.
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Affiliation(s)
- Qingyang Liu
- Department of Statistics, University of Connecticut, Storrs, Connecticut, USA
| | - Guanyu Hu
- Department of Statistics, University of Missouri - Columbia, Columbia, Missouri, USA
| | - Binqi Ye
- Boehringer Ingelheim (China), Shanghai, China
| | - Susan Wang
- Boehringer-Ingelheim Pharmaceutical Inc., Ridgefield, Connecticut, USA
| | - Yaoshi Wu
- Department of Statistics, University of Connecticut, Storrs, Connecticut, USA
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4
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Kundu MG, Samanta S, Mondal S. Review of calculation of conditional power, predictive power and probability of success in clinical trials with continuous, binary and time-to-event endpoints. HEALTH SERVICES AND OUTCOMES RESEARCH METHODOLOGY 2023. [DOI: 10.1007/s10742-023-00302-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
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5
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Affiliation(s)
- Charlotte Micheloud
- Charlotte Micheloud is Ph.D. student, Department of Biostatistics, Institute of Epidemiology, Biostatistics and Prevention, University of Zurich, Hirschengraben 84, 8001 Zurich, Switzerland
| | - Leonhard Held
- Leonhard Held is Professor, Department of Biostatistics, Institute of Epidemiology, Biostatistics and Prevention, University of Zurich, Hirschengraben 84, 8001 Zurich, Switzerland
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6
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Pilz M, Herrmann C, Rauch G, Kieser M. Optimal unplanned design modification in adaptive two-stage trials. Pharm Stat 2022; 21:1121-1137. [PMID: 35604767 DOI: 10.1002/pst.2228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Revised: 02/01/2022] [Accepted: 04/24/2022] [Indexed: 11/08/2022]
Abstract
Adaptive planning of clinical trials allows modifying the entire trial design at any time point mid-course. In this paper, we consider the case when a trial-external update of the planning assumptions during the ongoing trial makes an unforeseen design adaptation necessary. We take up the idea to construct adaptive designs with defined features by solving an optimization problem and apply it to the situation of unplanned design reassessment. By using the conditional error principle, we present an approach on how to optimally modify the trial design at an unplanned interim analysis while at the same time strictly protecting the type I error rate. This linking of optimal design planning and the conditional error principle allows sound reactions to unforeseen events that make a design reassessment necessary.
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Affiliation(s)
- Maximilian Pilz
- Institute of Medical Biometry, University Medical Center Ruprecht-Karls University Heidelberg, Heidelberg, Germany
| | - Carolin Herrmann
- Institute of Biometry and Clinical Epidemiology, Charité - Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
| | - Geraldine Rauch
- Institute of Biometry and Clinical Epidemiology, Charité - Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin, Berlin, Germany
| | - Meinhard Kieser
- Institute of Medical Biometry, University Medical Center Ruprecht-Karls University Heidelberg, Heidelberg, Germany
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7
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Herrmann C, Kieser M, Rauch G, Pilz M. Optimization of adaptive designs with respect to a performance score. Biom J 2022; 64:989-1006. [PMID: 35426460 DOI: 10.1002/bimj.202100166] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Revised: 02/09/2022] [Accepted: 02/12/2022] [Indexed: 11/08/2022]
Abstract
Adaptive designs are an increasingly popular method for the adaptation of design aspects in clinical trials, such as the sample size. Scoring different adaptive designs helps to make an appropriate choice among the numerous existing adaptive design methods. Several scores have been proposed to evaluate adaptive designs. Moreover, it is possible to determine optimal two-stage adaptive designs with respect to a customized objective score by solving a constrained optimization problem. In this paper, we use the conditional performance score by Herrmann et al. (2020) as the optimization criterion to derive optimal adaptive two-stage designs. We investigate variations of the original performance score, for example, by assigning different weights to the score components and by incorporating prior assumptions on the effect size. We further investigate a setting where the optimization framework is extended by a global power constraint, and additional optimization of the critical value function next to the stage-two sample size is performed. Those evaluations with respect to the sample size curves and the resulting design's performance can contribute to facilitate the score's usage in practice.
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Affiliation(s)
- Carolin Herrmann
- Institute of Biometry and Clinical Epidemiology, Charité - Universitätsmedizin Berlin, Berlin, Germany
| | - Meinhard Kieser
- Institute of Medical Biometry, University Hospital Heidelberg, Heidelberg, Germany
| | - Geraldine Rauch
- Institute of Biometry and Clinical Epidemiology, Charité - Universitätsmedizin Berlin, Berlin, Germany
| | - Maximilian Pilz
- Institute of Medical Biometry, University Hospital Heidelberg, Heidelberg, Germany
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8
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Anderson SF. Power(ful) myths: misconceptions regarding sample size in quality of life research. Qual Life Res 2021; 31:2917-2929. [PMID: 34716528 DOI: 10.1007/s11136-021-03020-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/13/2021] [Indexed: 11/25/2022]
Abstract
PURPOSE Carefully selecting the sample size for a research study is one of the most fundamental ways to utilize resources in an ethical manner, maximize impact and replicability, and minimize research waste when investigating questions relevant to health-related quality of life (HRQOL). Despite an increased focus on sample size in the methodological literature, the topic has received limited attention in the HRQOL field, and there are still misconceptions that can weaken even well-intentioned sample size planning. This article aims to highlight common misconceptions, provide accessible and non-technical corrections to these misconceptions, and show how HRQOL researchers can benefit from a more nuanced understanding of sample size planning. METHOD Misconceptions were identified broadly through examples within the health, psychology, and HRQOL literatures. In examining these misconceptions, study-level (e.g., missing data, multilevel designs, multiple reported outcomes) and field-level (e.g., publication bias, replicability) issues relevant to HRQOL research were considered. RESULTS Misconceptions include: (a) researchers should use rules of thumb or the largest sample size possible, (b) sample size planning should always focus on power, (c) planned power = actual power, (d) there is only one level of power per study, and (e) power is only relevant for the individual researcher. Throughout the article, major themes linked to these misconceptions are mapped onto recent HRQOL studies to make the connections more tangible. CONCLUSION By clarifying several challenges and misconceptions regarding sample size planning and statistical power, HRQOL researchers will have the tools needed to augment the research literature in effective and meaningful ways.
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Affiliation(s)
- Samantha F Anderson
- Department of Psychology, Arizona State University, 950 S. McAllister Ave, Tempe, AZ, 85287, USA.
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9
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Cook JA, Julious SA, Sones W, Hampson LV, Hewitt C, Berlin JA, Ashby D, Emsley R, Fergusson DA, Walters SJ, Wilson EC, MacLennan G, Stallard N, Rothwell JC, Bland M, Brown L, Ramsay CR, Cook A, Armstrong D, Altman D, Vale LD. Practical help for specifying the target difference in sample size calculations for RCTs: the DELTA 2 five-stage study, including a workshop. Health Technol Assess 2019; 23:1-88. [PMID: 31661431 PMCID: PMC6843113 DOI: 10.3310/hta23600] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
BACKGROUND The randomised controlled trial is widely considered to be the gold standard study for comparing the effectiveness of health interventions. Central to its design is a calculation of the number of participants needed (the sample size) for the trial. The sample size is typically calculated by specifying the magnitude of the difference in the primary outcome between the intervention effects for the population of interest. This difference is called the 'target difference' and should be appropriate for the principal estimand of interest and determined by the primary aim of the study. The target difference between treatments should be considered realistic and/or important by one or more key stakeholder groups. OBJECTIVE The objective of the report is to provide practical help on the choice of target difference used in the sample size calculation for a randomised controlled trial for researchers and funder representatives. METHODS The Difference ELicitation in TriAls2 (DELTA2) recommendations and advice were developed through a five-stage process, which included two literature reviews of existing funder guidance and recent methodological literature; a Delphi process to engage with a wider group of stakeholders; a 2-day workshop; and finalising the core document. RESULTS Advice is provided for definitive trials (Phase III/IV studies). Methods for choosing the target difference are reviewed. To aid those new to the topic, and to encourage better practice, 10 recommendations are made regarding choosing the target difference and undertaking a sample size calculation. Recommended reporting items for trial proposal, protocols and results papers under the conventional approach are also provided. Case studies reflecting different trial designs and covering different conditions are provided. Alternative trial designs and methods for choosing the sample size are also briefly considered. CONCLUSIONS Choosing an appropriate sample size is crucial if a study is to inform clinical practice. The number of patients recruited into the trial needs to be sufficient to answer the objectives; however, the number should not be higher than necessary to avoid unnecessary burden on patients and wasting precious resources. The choice of the target difference is a key part of this process under the conventional approach to sample size calculations. This document provides advice and recommendations to improve practice and reporting regarding this aspect of trial design. Future work could extend the work to address other less common approaches to the sample size calculations, particularly in terms of appropriate reporting items. FUNDING Funded by the Medical Research Council (MRC) UK and the National Institute for Health Research as part of the MRC-National Institute for Health Research Methodology Research programme.
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Affiliation(s)
- Jonathan A Cook
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK
| | - Steven A Julious
- Medical Statistics Group, School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - William Sones
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK
| | - Lisa V Hampson
- Statistical Methodology and Consulting, Novartis Pharma AG, Basel, Switzerland
| | - Catherine Hewitt
- York Trials Unit, Department of Health Sciences, University of York, York, UK
| | | | - Deborah Ashby
- Imperial Clinical Trials Unit, Imperial College London, London, UK
| | - Richard Emsley
- Department of Biostatistics and Health Informatics, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, UK
| | - Dean A Fergusson
- Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada
| | - Stephen J Walters
- Medical Statistics Group, School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Edward Cf Wilson
- Cambridge Centre for Health Services Research, Cambridge Clinical Trials Unit University of Cambridge, Cambridge, UK
- Health Economics Group, Norwich Medical School, University of East Anglia, Norwich, UK
| | - Graeme MacLennan
- Centre for Healthcare Randomised Trials, University of Aberdeen, Aberdeen, UK
| | - Nigel Stallard
- Warwick Medical School, Statistics and Epidemiology, University of Warwick, Coventry, UK
| | - Joanne C Rothwell
- Medical Statistics Group, School of Health and Related Research, University of Sheffield, Sheffield, UK
| | - Martin Bland
- Department of Health Sciences, University of York, York, UK
| | - Louise Brown
- MRC Clinical Trials Unit, Institute of Clinical Trials and Methodology, University College London, London, UK
| | - Craig R Ramsay
- Health Services Research Unit, University of Aberdeen, Aberdeen, UK
| | - Andrew Cook
- Wessex Institute, University of Southampton, Southampton, UK
| | - David Armstrong
- School of Population Health and Environmental Sciences, King's College London, London, UK
| | - Douglas Altman
- Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK
| | - Luke D Vale
- Health Economics Group, Institute of Health & Society, Newcastle University, Newcastle upon Tyne, UK
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10
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Anderson SF. Best (but oft forgotten) practices: sample size planning for powerful studies. Am J Clin Nutr 2019; 110:280-295. [PMID: 31131390 DOI: 10.1093/ajcn/nqz058] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Accepted: 03/18/2019] [Indexed: 11/14/2022] Open
Abstract
Given recent concerns regarding replicability and trustworthiness in several areas of science, it is vital to encourage researchers to conduct statistically rigorous studies. Achieving a high level of statistical power is one particularly important domain in which researchers can improve the quality and reproducibility of their studies. Although several factors influence statistical power, appropriate sample size planning is often under the control of the researcher and can result in powerful studies. However, the process of conducting sample size planning to achieve a specified level of desired statistical power is often complex and the literature can be difficult to navigate. This article aims to provide an approachable overview of statistical power and sample size planning, with emphasis on why statistical power is important for high-quality science. Thorough examples relevant to nutrition researchers are included to illustrate the process of sample size planning. Special consideration is also given to issues that may arise when conducting sample size planning in practice. The overarching goal is to provide nutrition researchers with the tools and expertise needed to conduct effective sample size planning for future studies.
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Anderson SF, Kelley K, Maxwell SE. Sample-Size Planning for More Accurate Statistical Power: A Method Adjusting Sample Effect Sizes for Publication Bias and Uncertainty. Psychol Sci 2017; 28:1547-1562. [DOI: 10.1177/0956797617723724] [Citation(s) in RCA: 164] [Impact Index Per Article: 23.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The sample size necessary to obtain a desired level of statistical power depends in part on the population value of the effect size, which is, by definition, unknown. A common approach to sample-size planning uses the sample effect size from a prior study as an estimate of the population value of the effect to be detected in the future study. Although this strategy is intuitively appealing, effect-size estimates, taken at face value, are typically not accurate estimates of the population effect size because of publication bias and uncertainty. We show that the use of this approach often results in underpowered studies, sometimes to an alarming degree. We present an alternative approach that adjusts sample effect sizes for bias and uncertainty, and we demonstrate its effectiveness for several experimental designs. Furthermore, we discuss an open-source R package, BUCSS, and user-friendly Web applications that we have made available to researchers so that they can easily implement our suggested methods.
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12
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Anderson SF, Maxwell SE. Addressing the "Replication Crisis": Using Original Studies to Design Replication Studies with Appropriate Statistical Power. MULTIVARIATE BEHAVIORAL RESEARCH 2017; 52:305-324. [PMID: 28266872 DOI: 10.1080/00273171.2017.1289361] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2016] [Accepted: 01/09/2017] [Indexed: 06/06/2023]
Abstract
Psychology is undergoing a replication crisis. The discussion surrounding this crisis has centered on mistrust of previous findings. Researchers planning replication studies often use the original study sample effect size as the basis for sample size planning. However, this strategy ignores uncertainty and publication bias in estimated effect sizes, resulting in overly optimistic calculations. A psychologist who intends to obtain power of .80 in the replication study, and performs calculations accordingly, may have an actual power lower than .80. We performed simulations to reveal the magnitude of the difference between actual and intended power based on common sample size planning strategies and assessed the performance of methods that aim to correct for effect size uncertainty and/or bias. Our results imply that even if original studies reflect actual phenomena and were conducted in the absence of questionable research practices, popular approaches to designing replication studies may result in a low success rate, especially if the original study is underpowered. Methods correcting for bias and/or uncertainty generally had higher actual power, but were not a panacea for an underpowered original study. Thus, it becomes imperative that 1) original studies are adequately powered and 2) replication studies are designed with methods that are more likely to yield the intended level of power.
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13
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Du H, Wang L. A Bayesian Power Analysis Procedure Considering Uncertainty in Effect Size Estimates from a Meta-analysis. MULTIVARIATE BEHAVIORAL RESEARCH 2016; 51:589-605. [PMID: 27485763 DOI: 10.1080/00273171.2016.1191324] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In conventional frequentist power analysis, one often uses an effect size estimate, treats it as if it were the true value, and ignores uncertainty in the effect size estimate for the analysis. The resulting sample sizes can vary dramatically depending on the chosen effect size value. To resolve the problem, we propose a hybrid Bayesian power analysis procedure that models uncertainty in the effect size estimates from a meta-analysis. We use observed effect sizes and prior distributions to obtain the posterior distribution of the effect size and model parameters. Then, we simulate effect sizes from the obtained posterior distribution. For each simulated effect size, we obtain a power value. With an estimated power distribution for a given sample size, we can estimate the probability of reaching a power level or higher and the expected power. With a range of planned sample sizes, we can generate a power assurance curve. Both the conventional frequentist and our Bayesian procedures were applied to conduct prospective power analyses for two meta-analysis examples (testing standardized mean differences in example 1 and Pearson's correlations in example 2). The advantages of our proposed procedure are demonstrated and discussed.
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Affiliation(s)
- Han Du
- a University of Notre Dame
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14
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Rufibach K, Burger HU, Abt M. Bayesian predictive power: choice of prior and some recommendations for its use as probability of success in drug development. Pharm Stat 2016; 15:438-46. [PMID: 27442271 DOI: 10.1002/pst.1764] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2015] [Indexed: 11/11/2022]
Abstract
Bayesian predictive power, the expectation of the power function with respect to a prior distribution for the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the prior. The density of power values induced by a given prior is derived analytically and its shape characterized. We find that for a typical clinical trial scenario, this density has a u-shape very similar, but not equal, to a β-distribution. Alternative priors are discussed, and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Kaspar Rufibach
- Department of Biostatistics, Hoffmann-La Roche Ltd, Basel, Switzerland.
| | | | - Markus Abt
- Department of Biostatistics, Hoffmann-La Roche Ltd, Basel, Switzerland
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15
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Funder DC, Levine JM, Mackie DM, Morf CC, Sansone C, Vazire S, West SG. Improving the Dependability of Research in Personality and Social Psychology. PERSONALITY AND SOCIAL PSYCHOLOGY REVIEW 2013; 18:3-12. [DOI: 10.1177/1088868313507536] [Citation(s) in RCA: 169] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this article, the Society for Personality and Social Psychology (SPSP) Task Force on Publication and Research Practices offers a brief statistical primer and recommendations for improving the dependability of research. Recommendations for research practice include (a) describing and addressing the choice of N (sample size) and consequent issues of statistical power, (b) reporting effect sizes and 95% confidence intervals (CIs), (c) avoiding “questionable research practices” that can inflate the probability of Type I error, (d) making available research materials necessary to replicate reported results, (e) adhering to SPSP’s data sharing policy, (f) encouraging publication of high-quality replication studies, and (g) maintaining flexibility and openness to alternative standards and methods. Recommendations for educational practice include (a) encouraging a culture of “getting it right,” (b) teaching and encouraging transparency of data reporting, (c) improving methodological instruction, and (d) modeling sound science and supporting junior researchers who seek to “get it right.”
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