Testing the Differential Effect of a Mathematical Background on Statistics Course Performance: An Application of the Chow-Test
Choudhury, Askar, Radhakrishnan, Ramaswamy, Journal of Economics and Economic Education Research
Identifying appropriate prerequisite course is a key ingredient 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) and DelMas 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. The course includes descriptive statistics, probability concepts, sampling processes, statistical inference, regression, and nonparametric procedures. Among the several available prerequisite courses we analyze the differential effect of Applied Calculus and Calculus-I on the Statistics course performance. Since, this will be fascinating to observe if there is any differential effect due to different arrangement of calculus course. If so, what is the propensity of the differential effect?
We hypothesize that students' performance in Statistics course as measured by the final course grade varies due to the diverse preparedness by different prerequisite courses. The question that we ask is that whether Applied Calculus or Calculus-I are availing themselves to the same background knowledge and prepare students equally for the Statistics course. Specifically, this research addresses the question; does the different mathematical background knowledge attained by students from Applied Calculus or Calculus-I create a differential effect on their performance in the Statistics course? Applied Calculus covers non-linear functions, intuitive differential, integral and multivariate calculus applications. Calculus-I covers Polynomial, exponential, logarithmic, and trigonometric functions; Differentiation with associated applications; Introduction to integration with applications.
Business and Economics students in general try to avoid (or delay) taking Statistics course. The fear of statistics may be a result of lack of acquaintance in mathematical thinking (Kellogg, 1939). Therefore, a proper prerequisite course that can build confidence against mathematical anxiety and develop mathematical thinking could help alleviate these problems. …