This study presents a set of data analysis approaches for single subject designs (SSDs). The primary purpose is to establish a series of statistical models to supplement visual analysis in single subject research using Bayesian estimation. Linear modeling approach has been used to study level and trend changes. I propose an alternate approach that treats the phase change-point between the baseline and intervention conditions as an unknown parameter. Similar to some existing approaches, the models take into account changes in slopes and intercepts in the presence of serial dependency. The Bayesian procedure used to estimate the parameters and analyze the data is described. Researchers use a variety of statistical analysis methods to analyze different single subject research designs. This dissertation presents a series of statistical models to model data from various conditions: the baseline phase, A-B design, A-B-A-B design, multiple baseline design, alternating treatments design, and changing criterion design. The change-point evaluation method can provide additional confirmation of causal effect of the treatment on target behavior. Software codes are provided as supplemental materials in the appendices. The applicability for the analyses is demonstrated using five examples from the SSD literature.