Small Sample Size Solutions

Researchers often have difficulties collecting enough data to test their hypotheses, either because target groups are small or hard to access, or because data collection entails prohibitive costs. Such obstacles may result in data sets that are too small for the complexity of the statistical model needed to answer the research question. This unique book provides guidelines and tools for implementing solutions to issues that arise in small sample research. Each chapter illustrates statistical methods that allow researchers to apply the optimal statistical model for their research question when the sample is too small. This essential book will enable social and behavioral science researchers to test their hypotheses even when the statistical model required for answering their research question is too complex for the sample sizes they can collect. The statistical models in the book range from the estimation of a population mean to models with latent variables and nested observations, and solutions include both classical and Bayesian methods. All proposed solutions are described in steps researchers can implement with their own data and are accompanied with annotated syntax in R. The methods described in this book will be useful for researchers across the social and behavioral sciences, ranging from medical sciences and epidemiology to psychology, marketing, and economics.

Prof. Dr. Rens van de Schoot works as a Full Professor teaching Statistics for Small Data Sets at Utrecht University in the Netherlands and as Extra-ordinary professor North-West University in South Africa. He obtained his PhD cum laude on the topic of applying Bayesian statistics to empirical data. Dr. Milica Miocevic is an Assistant Professor in the Department of Psychology at McGill University. She received her PhD in Quantitative Psychology from Arizona State University in 2017. Dr. Miocevic's research evaluates optimal ways to use Bayesian methods in the social sciences, particularly for mediation analysis.

Introduction (Van de Schoot and Miocevic) List of Symbols Part I: Bayesian solutions 1. Introduction to Bayesian statistics (Miocevic, Levy, and van de Schoot) 2. The role of exchangeability in sequential updating of findings from small studies and the challenges of identifying exchangeable data sets (Miocevic, Levy, and Savord) 3. A tutorial on using the WAMBS checklist to avoid the misuse of Bayesian statistics (van de Schoot, Veen, Smeets, Winter, and Depaoli) 4. The importance of collaboration in Bayesian analyses with small samples (Veen and Egberts) 5. A tutorial on Bayesian penalized regression with shrinkage priors for small sample sizes (van Erp) Part II: n=1 6. One by one: the design and analysis of replicated randomized single-case experiments (Onghena) 7. Single-case experimental designs in clinical intervention research (Maric and van der Werff) 8. How to improve the estimation of a specific examinee's (n=1) math ability when test data are limited (Lek and Arts) 9. Combining evidence over multiple individual analyses (Klaassen) 10. Going multivariate in clinical trial studies: a Bayesian framework for multiple binary outcomes (Kavelaars) Part III: Complex hypotheses and models 11. An introduction to restriktor: evaluating informative hypotheses for linear models (Vanbrabant and Rosseel) 12. Testing replication with small samples: applications to ANOVA (Zondervan-Zwijnenburg and Rijshouwer) 13. Small sample meta-analyses: exploring heterogeneity using MetaForest (van Lissa) 14. Item parcels as indicators: why, when, and how to use them in small sample research (Rioux, Stickley, Odejimi, and Little) 15. Small samples in multilevel modeling (Hox and McNeish) 16. Small sample solutions for structural equation modeling (Rosseel) 17. SEM with small samples: two-step modeling and factor score regression versus Bayesian estimation with informative priors (Smid and Rosseel) 18. Important yet unheeded: some small sample issues that are often overlooked (Hox) Index

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