  The multifractality of the critical eigenstate at the metal to insulator
transition (MIT) in the three-dimensional Anderson model of localization is
characterized by its associated singularity spectrum f(alpha). Recent works in
1D and 2D critical systems have suggested an exact symmetry relation in
f(alpha). Here we show the validity of the symmetry at the Anderson MIT with
high numerical accuracy and for very large system sizes. We discuss the
necessary statistical analysis that supports this conclusion. We have obtained
the f(alpha) from the box- and system-size scaling of the typical average of
the generalized inverse participation ratios. We show that the best symmetry in
f(alpha) for typical averaging is achieved by system-size scaling, following a
strategy that emphasizes using larger system sizes even if this necessitates
fewer disorder realizations.
