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.
Author(s): Rens van de Schoot
Series: European Association of Methodology
Publisher: Routledge
Year: 2020
Language: English
Pages: 270
City: London
Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Introduction
List of symbols
PART I:
Bayesian solutions
1. Introduction to Bayesian statistics
Introduction
Bayes’ theorem
Bayesian estimation
Conclusion
Note
References
2. The role of exchangeability in sequential updating of findings from small studies and the challenges of identifying exchangeable data sets
Introduction
Bayesian inference for exchangeable data sets
Relevant characteristics for establishing exchangeability
Conclusions and next steps
Notes
References
3. A tutorial on using the WAMBS checklist to avoid the misuse of Bayesian statistics
Introduction
Example data
WAMBS checklist
Does convergence remain after doubling the number of iterations?
Conclusion
Acknowledgement
Notes
References
4. The importance of collaboration in Bayesian analyses with small samples
Introduction
Latent growth models with small sample sizes
Empirical example: analysis plan
Empirical example: conducting the analysis
Debugging
Moving forward: alternative models
Conclusion
Acknowledgements
Note
References
5. A tutorial on Bayesian penalized regression with shrinkage priors for small sample sizes
Introduction
Running example: communities and crime
Software
Shrinkage priors
Practical considerations
Acknowledgement
Note
References
PART II: n = 1
6. One by one: the design and analysis of replicated randomized single-case experiments
Introduction
The single-case experiment
Design of single-case experiments
Analysis of single-case experiments
Conclusion
References
7. Single-case experimental designs in clinical intervention research
Introduction
Single-case experimental designs: definition and most important features
Clinical case example
Conclusion
References
8. How to improve the estimation of a specific examinee’s (n = 1) math ability when test data are limited
Introduction
Teacher knowledge
Steps of the expert elicitation instrument
Other (‘similar’) examinees
Conclusion
Acknowledgment
Note
References
9. Combining evidence over multiple individual analyses
Introduction
Informative hypotheses and Bayes factors
Data, model and hypotheses
Individual Bayes factors
Aggregating Bayes factors
Conclusion and limitations
References
10. Going multivariate in clinical trial studies: a Bayesian framework for multiple binary outcomes
Introduction
Decision rules
Data analysis
Computation in practice
Sample size considerations
Concluding remarks
Acknowledgement
References
PART III: Complex hypotheses and models
11. An introduction to restriktor: evaluating informative hypotheses for linear models
Introduction
Getting started
Example 1: Ordered-constrained means of a one-way ANOVA model
Example 2: Ordered-constrained means with effect sizes
Example 3: Order-constrained (standardized) linear regression coefficients
Example 4: Testing order constraints on newly defined parameters
Conclusion
Notes
References
12. Testing replication with small samples: applications to ANOVA
Introduction
Example: original study and its replication
Four replication methods
Discussion
Author note
Note
References
13. Small sample meta-analyses: exploring heterogeneity using MetaForest
Introduction
Models for meta-analysis
A
method for exploratory moderator selection
Using MetaForest for small samples
Final thoughts
References
14. Item parcels as indicators: why, when, and how to use them in small sample research
Introduction
Benefits of parceling
Building parcels
Conclusion
Acknowledgement
References
15. Small samples in multilevel modeling
Introduction
Multilevel regression models
Multilevel structural equation models
Bayes estimation
Discussion
References
16. Small sample solutions for structural equation modeling
Introduction
Some issues with small samples sizes in SEM
Possible solutions for point estimation
Small sample inference for SEM
Conclusion
References
17. SEM with small samples: two-step modeling and factor score regression versus Bayesian estimation with informative priors
Introduction
Simulation design
Results
Conclusion
Acknowledgement
Notes
References
18. Important yet unheeded: some small sample issues that are often overlooked
Introduction
The missing estimator: Ordinary Least Squares
The importance of assumptions of OLS and how to avoid making these assumptions
The importance of estimation methods and techniques
The importance of having ‘nice’ data
The importance of design
Conclusion
Note
References
Index
