Some Statistical Analyses of an Exam of a first course in Mathematics for Architects

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.