Qualitative knowledge is about types of things, and their excellences. There are many ways we humans produce qualitative knowledge about the world, and much of it is derived from non-quantitative sources (e.g., narratives, clinical experiences, intuitions). The purpose of my dissertation was to investigate the possibility of using Bayesian inferences to improve quantitative analysis in special education research with qualitative knowledge. It is impossible, however, to fully disentangle philosophy of inquiry, methodology, and methods. My evaluation of Bayesian estimators, thus, addresses each of these areas. Chapter Two offers a philosophical argument to substantiate the thesis that Bayesian inference is usually more applicable in education science than classical inference. I then moved on, in Chapter Three, to consider methodology. I used simulation procedures to show that even a minimum amount of qualitative information can suffice to improve Bayesian t-tests' frequency properties. Finally, in Chapter Four, I offered a practical demonstration of how Bayesian methods could be utilized in special education research to solve technical problems. In Chapter Five, I show how these three chapters, taken together, evidence that Bayesian analysis can promote a romantic science of special education - i.e., a non-positivistic science that invites teleological explanation. These explanations are often produced by researchers in the qualitative tradition, and Bayesian priors are formal mechanism for strengthening quantitative analysis with such qualitative bits of information. Researchers are also free to use their favorite qualitative methods to elicit such priors from experts.