  In machine learning, supervised classifiers are used to obtain predictions
for unlabeled data by inferring prediction functions using labeled data.
Supervised classifiers are widely applied in domains such as computational
biology, computational physics and healthcare to make critical decisions.
However, it is often hard to test supervised classifiers since the expected
answers are unknown. This is commonly known as the \emph{oracle problem} and
metamorphic testing (MT) has been used to test such programs. In MT,
metamorphic relations (MRs) are developed from intrinsic characteristics of the
software under test (SUT). These MRs are used to generate test data and to
verify the correctness of the test results without the presence of a test
oracle. Effectiveness of MT heavily depends on the MRs used for testing. In
this paper we have conducted an extensive empirical study to evaluate the fault
detection effectiveness of MRs that have been used in multiple previous studies
to test supervised classifiers. Our study uses a total of 709 reachable mutants
generated by multiple mutation engines and uses data sets with varying
characteristics to test the SUT. Our results reveal that only 14.8\% of these
mutants are detected using the MRs and that the fault detection effectiveness
of these MRs do not scale with the increased number of mutants when compared to
what was reported in previous studies.
