Medication non-adherence is a major reason for a lack of effectiveness of efficacious drug regimens. Adherence distributions are J-shaped with many taking their medication completely, a large number taking none, and a small number taking it intermittently. Comparisons are typically made using parametric and non-parametric techniques, or by dichotomization, which all have limitations. Parametric techniques may be inappropriate as the assumptions (e.g., normality) are violated and transformations fail; Central tendency measures and non-parametric techniques do not adequately depict the distribution; and, dichotomization results in information loss, making small improvements indiscernible. We propose an analytic technique using a beta mixture characterized by pb(1,b)+(1-p)b(a,1), producing a J-shaped distribution. The proportion of values in each tail will be determined by p. The EM algorithm will be used to produce parameter and standard error estimates. This technique will allow for the description of the distribution's shape and comparisons of parameter estimates for two distributions to determine if two interventions differ. We will assess, via simulation studies, alpha levels and power for this new method as compared to other standard methods.