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AbstractWhile the Bayesian parameter estimation has gained a wider acknowledgement among political scientists, they seem to have less discussed the Bayesian version of hypothesis testing. This paper introduces two Bayesian approaches to hypothesis testing: one based on estimated posterior distributions and the other based on Bayes factors. By using an example based on a linear regression model, I demonstrate similarities and differences not only between the null‐hypothesis significance tests and Bayesian hypothesis tests, but also those among two different Bayesian approaches, which are also critically discussed.

AbstractThe traditional frequentist approach to hypothesis testing has recently come under extensive debate, raising several critical concerns. Additionally, practical applications often blend the decision-theoretical framework pioneered by Neyman and Pearson with the inductive inferential process relied on the p-value, as advocated by Fisher. The combination of the two methods has led to interpreting the p-value as both an observed error rate and a measure of empirical evidence for the hypothesis. Unfortunately, both interpretations pose difficulties. In this context, we propose that resorting to confidence distributions can offer a valuable solution to address many of these critical issues. Rather than suggesting an automatic procedure, we present a natural approach to tackle the problem within a broader inferential context. Through the use of confidence distributions, we show the possibility of defining two statistical measures of evidence that align with different types of hypotheses under examination. These measures, unlike the p-value, exhibit coherence, simplicity of interpretation, and ease of computation, as exemplified by various illustrative examples spanning diverse fields. Furthermore, we provide theoretical results that establish connections between our proposal, other measures of evidence given in the literature, and standard testing concepts such as size, optimality, and the p-value.

AbstractConjoint analysis is widely used for estimating the effects of a large number of treatments on multidimensional decision-making. However, it is this substantive advantage that leads to a statistically undesirable property, multiple hypothesis testing. Existing applications of conjoint analysis except for a few do not correct for the number of hypotheses to be tested, and empirical guidance on the choice of multiple testing correction methods has not been provided. This paper first shows that even when none of the treatments has any effect, the standard analysis pipeline produces at least one statistically significant estimate of average marginal component effects in more than 90% of experimental trials. Then, we conduct a simulation study to compare three well-known methods for multiple testing correction, the Bonferroni correction, the Benjamini–Hochberg procedure, and the adaptive shrinkage (Ash). All three methods are more accurate in recovering the truth than the conventional analysis without correction. Moreover, the Ash method outperforms in avoiding false negatives, while reducing false positives similarly to the other methods. Finally, we show how conclusions drawn from empirical analysis may differ with and without correction by reanalyzing applications on public attitudes toward immigration and partner countries of trade agreements.