  We propose a detailed investigation of the schematic mode-coupling approach
to experimental data, a method based on the use of simple mode-coupling
equations to analyze the dynamics of supercooled liquids. Our aim here is to
clarify different aspects of this approach that appeared so far uncontrolled or
arbitrary, and to validate the results obtained from previous works. Analyzing
the theoretical foundations of the approach, we first identify the parameters
of the theory playing a key role and obtain simple requirements to be met by a
schematic model for its use in this context. Then we compare the results
obtained from the schematic analysis of a given set of experimental data with a
variety of models and show that they are all perfectly consistent. A number of
potential biases in the method are identified and ruled out by the choice of
appropriate models. Finally, reference spectra computed from the mode-coupling
theory for a model simple liquid are analyzed along the same lines as
experimental data, allowing us to show that, despite the strong simplification
in the description of the dynamics it involves, the method is free from
spurious artifacts and provides accurate estimates of important parameters of
the theory. The only exception is the exponent parameter, the evaluation of
which is hindered, as for other methods, by corrections to the asymptotic laws
of the theory present when the dynamics is known only in a limited time or
frequency range.
