Comparison of two independent populations of compositional data with positive correlations among components using a nested dirichlet distribution.

Compositional data are multivariate data made up of components that sum to a fixed value. Often the data are presented as proportions of a whole, where the value of each component is constrained to be between 0 and 1 and the sum of the components is 1. There are many applications in psychology and other disciplines that yield compositional data sets including Morris water maze experiments, psychological well-being scores, analysis of daily physical activity times, and components of household expenditures.