Some Statistical analyses of an Exam of a first course in Mathematics for Architects
Keywords:
Item Response Model, Tandem Analysis, Exams, Math for Architecture, AssessmentAbstract
We present some statistical analyses to evaluate a data set, obtained from exams based on multiple response
tests, considering two methods, based on different rationale. Tandem Analysis, an exploratory technique consisting
in a Correspondence Analysis followed by a Hierarchical Classification, and the Psychometric Analysis that is based
on both Classical and Item Response Theory Analysis were considered. As a case study, we used a data set of a final
examination of Basic Mathematics, a test of 46 items, submitted to 180 students in Architecture. As results, the
Tandem Analysis showed a relatively independent behaviour of small groups of items, correlated with at least three
distinct factors, and partitions in 4 and 8 classes of the students, according to their performance. The Psychometric
analysis showed that both the raw and the Rasch scores of the tests were normal, presented high reliability, and
confirmed that the test structure was not unidimensional. In addition, the Item analysis indicated that the test
could be improved by eliminating some items, whose behaviour was not in agreement with the others. Eventually,
the exploratory analysis provides an interesting framework in which the psychometric analysis gives more details
that may be taken as a guide to improve the elaboration of exams.
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