The focus of this dissertation pertains to effective statistical analysis of cognition at the individual level. The first chapter challenges conventional wisdom for response time analysis by investigating whether there is any benefit to log or reciprocal transforming response times when doing a conventional t-test. The second chapter introduces two models for paired comparison data based on Cultural Consensus Theory. Through hierarchical Bayesian modeling, these models allow for recovery of parameters describing both group level and individual level opinion, tendency toward agreement, and consistency of evaluation as it pertains to the items being compared. The third chapter offers critique and improvements to individual-level True and Error analysis, a modern statistical framework for the evaluation of concurrent sets of preferences. A Hierarchical Bayesian implementation of the model is introduced, offering substantial gains in statistical power and accuracy in parameter estimates. Finally, the fourth chapter is an application of the methodology proposed in the third chapter. Specifically, the model is applied to the study of transitivity of preference in the domains of probabilistic and temporal discounting. Many instances of violations of transitivity were found at the individual level for the domain of probabilistic discounting and for the case where temporally and probabilistically discounted options were compared, with over 80\% of people showing strong evidence for transitivity violations in at least one case.