Intracellular cargos that are transported by groups of molecular motors often display bidirectional movement. This can be seen experimentally by tracking the trajectories of individual cargos in vivo. Typically, the cargo trajectories display many turning events that result from the stochastic nature of the involved motor processes. In this paper, we simulate cargo trajectories for different binding mechanisms. We introduce a series of statistical tools to analyze and quantitatively characterize these trajectories. As we demonstrate for specified single-motor properties, the novel statistical methods allow us to quantitatively distinguish between different models for bidirectional transport. In this way, the tools provide a quantitative connection between the statistical properties of the cargo trajectories and the molecular properties of the motor proteins. Such methods are also applicable to experimentally measured cargo trajectories and should be helpful in elucidating the mechanisms that lead to bidirectional transport.