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It is possible to apply a Bayesian approach in mixed methods instead of using classical/frequentists statistical analyses that rely on Null Hypothesis Significance Testing. Doing so can yield a number of advantages, including quantitizing prior (i.e., contextual or qualitative) information that might yield more flexible and accurate estimation. This paper therefore will describe the advantages of using qualitative information to establish a Bayesian prior (i.e., quantitizing qualitative information that can be used in estimation), thereby introducing the concept of Fully Integrated Bayesian Thinking (FIBT). The paper will then demonstrate how FIBT can be used to address two longstanding difficulties in the social sciences: (a) dealing with delayed treatment effects in single-case designs and (b) ignoring qualitative information in meta-analyses.