We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first recall a classification of effective models based on the requirement of anomaly cancellation and illustrate the general classification with the example of a quantum Hall fluid at filling factor ν=2/3. We show that, in this example, it is impossible to describe the edge states with only one chiral channel and that there are several inequivalent models of the edge states with two fields. We focus our attention on the four simplest models of the edge states of a fluid with ν=2/3 and evaluate charges and scaling dimensions of quasiparticles. We study transport through an electronic Mach-Zehnder interferometer and show that scaling properties of the Fourier components of Aharonov-Bohm oscillations in the current provide information about the electric charges and scaling dimensions of quasiparticles. Thus, Mach-Zehnder interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor. They, therefore, can be used to test fundamental postulates underlying the low-energy effective theory of edge states. An important ingredient of our analysis is the tunneling Hamiltonian of quasiparticles, the form of which is discussed in detail.