Abstract

With the increased use of Bayesian informative hypothesis testing, practical, philosophical and methodological questions arise. This dissertation addresses a few of these questions. One step in the research cycle is to collect data for hypothesis testing. The amount of data required to answer a research question depends on the value
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of making wrong conclusions. The link between sample size, power and error probabilities is well-researched in the NHST framework. In Bayesian statistics research this relationship is less discussed and the value of power and unconditional error probabilities are debated. Chapter 2 presents four sample size determination methods for informative hypothesis testing by means of Bayes factors. The value of power and (un)conditional error probabilities and their link with sample size for Bayesian hypothesis tests are discussed. Another step in the research cycle is to translate the results from a statistical analysis into a conclusion. The analysis should match the research question to provide a sensible conclusion. Many hypothesis tests concern the presence and direction of *population* effects. However, in practice the conclusions from these hypothesis tests often are at the *individual* level. For example, after analyzing the effectiveness of a medication in the population, it is prescribed to individuals. The average effect does not imply the medicine works for all individuals. In many situations the main interest is in the individual effects rather than population effects. Chapters 3 and 4 describe how Bayesian hypothesis testing can be used to synthesize the results from multiple individual analyses. Bayesian statistics can be used to continuously add data and sequentially update knowledge about population effects. This process is called updating. Alternatively, data from multiple individuals can be analyzed separately and combined to learn about how the homogeneity (similarity) of individual effects. Chapter 3 presents the methodology and Chapter 4 is a hands-on description for how to execute such an analysis. For Chapter 2 an R package has been developed, and for Chapter 3 an R Shiny application has been developed. Both pieces of software are presented in Chapter 6. Chapter 5 discusses the updating cycle in Bayesian statistics and focuses on the starting point of an updating cycle. The information in a Bayes factor is useful to describe how we can update our knowledge. However, knowing the rate with which the relative belief for two hypotheses changes is meaningless if the starting point is unknown. Chapter 5 therefore discusses the importance of prior probabilities and how to specify these for a set of hypotheses. Chapters 7 and 8 present applied research where informative hypotheses are tested with Bayes factors. These are examples of research that commonly are analyzed with NHST and are thus exemplary in what the possibilities with informative hypothesis testing are. In Chapter 7 informative hypotheses are formulated to analyze the data from a repeated measures experiment. Chapter 8 evaluates the presence of a mediated effect at the the individual level by means of Bayesian informative hypothess tests.
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