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Many
researchers know the superiority of the item response theory (IRT)
over the classical test theory (CTT) from a detailed test-evaluation
viewpoint. However, teachers are still reluctant to use the IRT
as a daily testing tool. The primary objective of this paper is
to find the difference between the CTT and the IRT. In particular,
we focus on the difference in ability evaluation. We compared the
CTT and IRT evaluated abilities by using the hypothetically assumed
abilities that are mimicked to a real case. By using a simulation
study, we found that the IRT is superior to the CTT to some extent.
The CTT uses pre-assigned allotments contrary to the IRT which
has no allotment concept. However, if we regard the ability evaluation
by the IRT as the standard, we can find the most appropriate allotments
in the CTT so that the total scores of the CTT are adjusted as
close as possible to the abilities obtained by the IRT. This is
a kind of allotment optimization problem. We show the methodology
in this paper. By applying our methodology to some simulation cases
that mimic the real data case, we found an intriguing feature with
respect to the pre-assigned allotments. If teachers want to raise
the examination pass rate, we guess that they give higher scores
than the actual scores achieved by students; we call this jacking-up.
Using the allotment optimization, we have found that jacking-up
causes higher allotments to easier problems in the CTT.
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