  We investigate the weak measurement experiment demonstrated by Ritchie et al.
[N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107
(1991)] from the viewpoint of the statistical hypothesis testing for the
weak-value amplification proposed by Susa and Tanaka [Y. Susa and S. Tanaka,
Phys. Rev. A 92, 012112 (2015)]. We conclude that the weak-value amplification
is a better method to determine whether the crystal used in the experiment is
birefringent than the measurement without postselection, when the angles of two
polarizers are almost orthogonal. This result gives a physical description and
intuition of the hypothesis testing and supports the experimental usefulness of
the weak-value amplification.
