Bayesian Approaches to Imputation, Hypothesis Testing, and Parameter Estimation

This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory‐driven substantive hypotheses without a default null hypothesis, and for extending the findings of meta‐analyses to Bayesian estimations of parameters hypothesized to be larger or smaller than those derived from earlier research summaries. Missing data is examined by taking a complete data set and decimating it to simulate a missing at random data set, one common in longitudinal research. Data imputation is then applied to replace the missing data. Comparisons of the full and replaced data sets are made to show that valid inferences about change are possible after imputation of missing data has taken place. The second application of Bayesian inference is demonstrated with the use of a confirmatory analysis of variance approach in which theory‐driven ordered prior hypotheses about mean differences are postulated before the means are compared. Posterior model probabilities and Bayes Factors are discussed as criteria for supporting or refuting the hypothesized mean differences. The third application of Bayesian analysis takes the results of a validity generalization meta‐analysis of aptitude for foreign language learning and tests if a median parameter estimate derived from the validity generalization will be corroborated against data from a language categorized as difficult to learn.