Testing the Differential Effect of a Mathematical Background on Statistics Course Performance: An Application of the Chow-Test

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ABSTRACT

This paper focuses on understanding the differential effect of students' mathematical background (prerequisite) knowledge on Statistics course. Introductory Statistics is one of the required courses for business and economics majors. Students can choose one of several mathematics based prerequisite courses to gain necessary background knowledge for the Statistics course. Among several possible prerequisite courses, we considered only two different calculus courses as background knowledge for Statistics course to compare; namely Applied Calculus and Calculus-I. Students' success on subsequent course is greatly affected by the prerequisite courses taken by students. Mathematical topics vary widely among these courses providing different breadth of background knowledge to prepare students for the Statistics course. Therefore, the objective of this research is to observe the significance and magnitude of differential effect of two different calculus courses on the Statistics course performance.

Chow test is being applied through regression models provided consistent conclusions about the significance and differential effect of mathematical background knowledge on the performance of Statistics course. Specifically, we have found that students who took the Calculus-I received higher grades on average in Statistics course than did students who took Applied Calculus. Thus, students with added traditional calculus orientation do have greater statistical proficiency. Furthermore, the analysis also reveals that students' are situated in an advantageous position when taking Calculus-I than with Applied Calculus.

INTRODUCTION

Identifying appropriate prerequisite course is a key ingrethent in designing the optimum curriculum program. An academic advisor's primary challenge is to match students' background knowledge with the courses they are taking. Identifying the most suitable course among the several available alternative prerequisite courses to meet students' need is a source of continuous debate among the academicians. This paper addresses the issue of students with different mathematical background perform differently in Statistics course. Higgins (1999) recognized that statistical reasoning should be considered an important component of any undergraduate program. Further discussion on statistical reasoning can be found in Garfield (2002) andDelMas et. al. (1999). Several different factors may affect students' performance (Dale & Crawford, 2000) in a course, including students' background knowledge. Therefore, understanding (Choudhury, Hubata& St. Louis, 1999) and acquiring the proper background knowledge is the primary driver of success (Bagamery, Lasik & Nixon, 2005; Sale, Cheek & Hatfield, 1999).

Students' performance (Trine & Schellenger, 1999) in a course is primarily affected by the prerequisite courses taken that fabricate their background knowledge. Because of their diverse level of preparedness and accumulated background knowledge that builds their long-term human capital, differential effect that is attributable to different perquisite courses can be evaluated through students' performance on subsequent courses. Literatures in this area of research offer little guidance, as to which prerequisite is more appropriate. Performance measures of prerequisite courses have been studied in various disciplines (Buschena & Watts, 1999; Butler, et. al., 1994; Cadena et. al., 2003). A remarkable discussion on the effect of prerequisite courses has been found in Potolsky, et. al. (2003).

For this study, data were collected from a Mid- Western university. Statistics is a required course for all business and economics majors at this university. Statistics course stresses application of statistical concepts to decision problems facing business organizations. All sections of this course taught at the college of business use a common text book and cover the same basic topics. …