Electronic Proceedings of the Twentyeighth Annual International Conference on Technology in Collegiate MathematicsAtlanta, Georgia, March 1013, 2016Paper A004
This is an electronic reprint, reproduced by permission of Pearson Education Inc. Originally appeared in the Proceedings of the Twentyeighth Annual International Conference on Technology in Collegiate Mathematics, ISBN 013480029X, Copyright (C) 2017 by Pearson Education, Inc. 
Testing Unfairness  Mathematics and Simulations 
Click to access this paper:

This paper examines some novel issues of testing unfairness from perspectives of the student, teacher,
but mostly the test itself. The literature usually examines testing unfairness between various groups, considering
mainly group demographics. We consider cognitively differentiated groups and test difficulty to examine how
groups perform on a particular test, both having defined distributions of ability and difficulty, respectively. Even
controlling the statistical parameters of the test and/or the group, there can be vast differences in outcomes, i.e.
exam averages. This holds even for high stakes testing, leading to the reality grades are almost always
'adjusted' to conform to testing expectations, i.e. we curve exam scores. In this section, we consider yet another
aspect of unfairness, and that is with the numbers embedded in the test itself, and how it affects class grades
with respect to class parameters. The two principle parameters about the student are the average ability and the
variation of those abilities. For the test, the two principle parameters are the average item difficulty and its
variation. However, we need also consider the actual distributions of the student abilities and the test
difficulties. These must be comingled in an intuitive manner. Various types of distributions of these
populations and difficulties are considered. In addition, we need to model the actual densities of student
abilities and item difficulties given the numbers of students and test items. For tests given to a relatively small
number of students, there are other considerations such as the need to use simulations. We discuss the
sensitivity of grades to parameters, distribution of grades, the effect of a small number of test takers, and the
relative variation in standardized tests.
Keyword(s): assessment