As more data on exoplanets have been collected, some apparent correlations between planetary and stellar properties have started to emerge. However, the true nature of such correlations is often unclear as stellar properties are often interrelated. In particular, it is unresolved whether these correlations are due to the age of the system — pointing to evolution over time being an important factor — or other parameters to which the age may be related, such as stellar mass or stellar temperature. The situation is complicated further by the possibilities of selection biases, small number statistics, uncertainties in stellar age, and orbital evolution timescales that are typically much shorter than the range of observed ages. We have developed a Bayesian statistical framework to assess the robustness of such observed correlations and to determine whether they are indeed due to evolutionary processes, are more likely to reflect different formation scenarios, or are merely coincidental. We have previously applied this framework to the cases of 2:1 resonances, stellar obliquities, and hot Jupiter eccentricities. We present an improved analysis using this framework that more formally incorporates measurement uncertainties. We also analyze updated samples for the 2:1 resonances and stellar obliquities cases, in order to take advantage of additional exoplanet discoveries as well as better stellar age measurements. Finally, we are using our framework to address the Kepler dichotomy, investigating whether the apparent excess in observed singly-transiting planets in the Kepler sample is due to dynamical interactions exciting initially coplanar systems to high mutual inclinations over time, or due to differing protoplanetary disk conditions that yield an abundance of systems that are singly-transiting from the start.