The purpose of this study is to find out whether there is a difference between item-test functions and the level of their relative efficiency which are estimated according to the Item Response Theory among the tests which measure similar cognitive skills related to success in mathematics, and in which multiple-choice and constructed response items are employed together with varying percentages. For that purpose, item and test information functions were estimated and relative efficiency indices were calculated through responses given to four mixed item tests, among the items within TIMSS 2007 Maths test booklet #2, the test length (number of items: 15 and 25) and open-ended item percentages (20% and 40%) of which were different. Parameter estimations were carried out via BILOG-MG software. Research data were obtained from 320 eight-grade students who participated in TIMMS 2007 maths application from Turkey and who were given the booklet #2, via the official webpage of OECD (http://timss.bc.edu/). At the end of the research, it is determined that the test composed of constructed response items yields more information in terms of students level of competence in mathematics than the one composed of multiple-choice items. Relative efficiency values indicate that the test composed of open-ended items is the most efficient of all tests.
Key words: Mixed Item Tests, Item Response Theory, Test Information Function, Relative Efficiency
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