In our three dimensional world, particles are either bosons or fermions. This picture changes when we restrict systems to live in two (spatial) dimensions. In particular, in two-dimensional strongly correlated systems, topological phases of matter can host quasi-particles that carry both fractional charge as well as fractional statistics. The latter means that the wave function gets multiplied by a phase under exchange of two particles, rather than a mere sign (for fermions) or no change at all (for bosons). Interestingly, the statistics can even be non-abelian, which means that the way the wave function (or rather the wave vector in this case) depends on the order in which the exchanges are preformed. It has been proposed that systems with non-abelian statistics can be used for quantum information and computation processes.' The prototypical examples for such systems are fractional quantum Hall states, which will be the focus of this project. We recently proved a spin-statistics theorem for quantum Hall systems directly from the microscopic theory. This theorem relates the exchanges statistics of the two quasi-particles, to the spin of individual quasi-particles. That is, the inherently non-local exchange statistics can be calculated form the local spin of quasi-particles. Obtaining the spin of the quasi-particles can in most cases not be done analytically. For wave functions that can be evaluated quickly, monte-carlo methods can be used. In this project, however, we will focus on quantum Hall wave functions that can not be evaluated quickly, namely the Read-Rezayi states (which host quasi-particles that are universal for quantum computation) and the (properly projected) Jain states, which describe the majority of quantum Hall plateaux observed in the lowest Landau level. For these states, monte-carlo techniques can not be used. Instead, we will use the matrix product state formulation of the Read-Rezayi and Jain states, which can be obtained from the underlying conformal field theory formulation. The results of the analysis will be the statistics properties of the quasi-holes appearing in these states. These can be obtained analytically, but only under the (unproven!) assumption that under the exchange, the Berry phase associated with the exchange is zero. By making use of the spin-statistics relation, we avoid this problem. Or, turning the argument around, our results, if they agree with the analytic results, show that the Berry phase associated with the quasi-particle exchange vanishes, which is a long-standing problem for the Read-Rezayi and Jain states (because of the absence of a plasma analogy).