  We formulate a method allowing to confirm or exclude the alternative models
of material properties at some definite confidence level in experiments on
measuring the Casimir force. The method is based on the consideration of
differences between the theoretical and mean measured quantities and the
confidence intervals for these differences found at sufficiently high or low
confidence probabilities. The developed method is applied to the data of four
recent experiments on measuring the gradient of the Casimir force by means of a
dynamic atomic force microscope. It is shown that in experiments with Au-Au and
Ni-Ni test bodies, where the Drude model approach is excluded at a 95%
confidence level, the plasma model approach agrees with the data at higher than
90% confidence. In experiments using an Au sphere interacting with either a Ni
plate or a graphene-coated substrate the measurement data agree with the common
prediction of the Drude and plasma model approaches and theory using the
polarization tensor at 90% and 80% confidence levels, respectively.
