How Much Math Do Students Need to Succeed in Business and Economics Statistics? An Ordered Probit Analysis

Abstract

Because statistical analysis requires the ability to use mathematics, students typically are required to take one or more prerequisite math courses prior to enrolling in the business statistics course. Despite these math prerequisites, however, many students find it difficult to learn business statistics.

In this study, we use an ordered probit model to analyze the impact of alternative prerequisite math course sequences on the grade performance of 1,684 business and economics statistics students at a large Midwestern university. In addition, we show how imposing a minimum grade requirement of C- for the math prerequisite course would influence student success in the business statistics course. Although several studies have examined the impact of different math skills, our study is the first to provide a detailed analysis of the impact of different prerequisite math course sequences on student performance in business statistics. We demonstrate that, other things the same, taking more math credit hours, taking math courses that emphasize calculus, and imposing a minimum grade of C- on the prerequisite math course have significant positive impacts on student grade performance in the business and economics statistics course.

• Introductory business statistics
• Math prerequisites
• Math topics
• Student performance
• Minimum prerequisite math grade requirement

Acknowledgments

We want to thank Janice Replogle, formerly the Director of Undergraduate Programs, College of Business, for her interest and support for this study and Dr. Tung Liu, Chair of the Economics Department, for patiently guiding us through the complexities of probit analysis. We also want to thank Michael T. Costello (University Computing Services) for providing us with the student data and the College of Business 2005 Summer Faculty Research Program for financial support at an early stage of this study. We would also like to thank session participants at the Eastern Economic and Midwest Economics Associations' 2008 Annual Meetings for their insightful comments. Finally, we would like to acknowledge the detailed suggestions from two anonymous referees that materially improved our paper.

Notes

1 Norris and Hudson (1999), p. 233.

2 For discussion of statistics anxiety, see Onwuegbuzie and Wilson (2003). For a small sample of the vast literature on how to improve statistics instruction, see Becker (1987, 1998), Becker and Greene (2001), Carlson (1999), Gandhi et al. (1991), Hakeem (2001), Hillmer (1996), McAlevey et al. (2001), and Parr and Smith (1998). For discussion of inadequate math preparation prior to entering college, see, Kronholz (2004) and Tomsho (2006). Finally, for a discussion of inadequate math prerequisites, see Green et al. (2007).

3 We exclude from this study both the students who did not complete the course (who received a W) and those who are taking it for the second or third time.

4 See, for example, Johnson and Kuennen (2006), Larson (2003) and Rochelle and Dotterweich (2007).

5 Green et al. (2007) examined the impact of prerequisite math course changes on the DFW rate using a binary probit analysis. They did not examine the letter grade performance of students in the business statistics course.

6 It excludes 174 transfer/transient students who completed ECON 221 but who had taken their prerequisite math courses elsewhere and 157 students who received a W in ECON 221 because they withdrew from the course before the end of the semester.

7 Other studies have noted similarly low levels of performance for business statistics students. See, for example, Green et al. (2007), Hakeem (2001), Keeler and Steinhorst (1994), and Lewis et al. (2005).

8 They are also required to complete two courses in each of accounting, economics, and English and a computer skills course.

9 The number of credit hours and the academic units for the course are identical.

10 MATHS 132 was not offered after the Spring 2004 semester.

11 The credit hours listed for the various math sequences are the maximum that students would have to take. They were allowed to enroll in MATHS 131, MATHS 135, MATHS 161 or MATHS 165 without taking all the math prerequisites for these courses if they had sufficient background in algebra and trigonometry as evidenced by their high school record, SAT/ACT score, and/or score on the mathematics placement test, or permission from the chair of the mathematics department.

12 Transitional period for change in math prerequisites in Fall 2004. See text for explanation.

13 MATHS 131 was only permitted as the prerequisite math class for business statistics in the 2004/05 academic year. However, comparison of MATHS 131 with the other prerequisite math courses is particularly relevant because, initially, discussion in the college curriculum committee favored simply dropping MATHS 132 and making MATHS 131 the prerequisite math course.

14 There is a third important difference between the math courses generally taken by pre-business students (MATHS 131/132 and 135) and math and science students (MATHS 161 and 165). The former classes are generally taught by contract faculty, while the latter courses are typically taught by tenure-track faculty.

15 The error term is assumed to be normally distributed with the usual properties.

16 In our preliminary research, we examined the impact of the student's math SAT score, gender and participation in varsity athletics which are often used in student performance studies. However, none of these variables were statistically significant and, therefore, we excluded them from our model.

17 For a discussion of the impact of increased class time on math skills, see Toppo (2007).

18 For example, see Borde et al. (1998), Brasfield et al. (1992), Butler et al. (1998), Didia and Hasnat (1998), Ely and Hittle (1990), Green et al. (2007), Haley et al. (2007) and Von Allmen (1996).

19 See, for example, Austin and Gustafson (2006), Garces-Ozanne (2004), Green et al. (2007), and Terry and Galchus (2003).

20 Kennedy (1998), p. 236.

21 Another model used in such studies is the ordered logit model. The probit model is used if the cumulative density function for the error term is assumed to follow a normal distribution. The logit model is used if the cumulative density function for the error term is assumed to follow a logistic distribution. The probit and logit models generally produce similar results. See, for example, Greene (2008), p. 832 or Kennedy (1998), p. 247.

22 Kennedy (1998), p. 236.

23 For detailed discussion of probit and logit model estimation, see Greene (2008), chapter 23 or Wooldridge (2009), chapter 17.

24 * denotes significance at the .01 level; ** denotes that the pair are jointly significant at the .05 level (F-test for redundant variables).

25 Wooldridge (2009), p. 580.

26 Kennedy (1998), p. 238.

27 See Kennedy (1998), p. 239; Wooldridge (2009), pp. 580-1.

28 Kennedy (1998), p. 239.

29 Results from the default model are available from the authors by request.

30 For references showing how these probabilities are derived from the estimated coefficients and the limit points, see EViews (2007), pp. 226–7 or Greene (2008) pp. 831-832.

31 These conditional probabilities for the designated math sequence and math course are estimated with the other explanatory variables valued at their mean values.

32 The increase was even more spectacular for MATHS 165 but, once again, this result is produced by the size of the negative estimated math grade interaction term for D165M.

33 The changes in probabilities for a one-unit change in GPA are calculated holding other explanatory variables constant at their mean values. The changes in probabilities for D131 through D165 are calculated by subtracting the probabilities for MATHS 132 from those for MATHS 131 through 165, respectively, in column 2 of Table 6. To see how these marginal probabilities are calculated, see Greene (2008), p. 833-4.

34 Because the numbers shown in the Table are changes in the probabilities of earning the designated statistics grades, they must necessarily sum to zero.

35 See Yang and Raehsler (2005, p. 8) for very similar results for the marginal impact of GPA on intermediate microeconomics grades.

36 Here the one-unit change is the change in the appropriate dummy variable from 0 to 1.

37 For this reason, colleges and universities often impose minimum grade requirements on student performance in specific courses and minimum GPA requirements for entry into many degree programs. For example, the College of Business currently requires students to earn a minimum grade of C in the prerequisite math course, a minimum GPA of 2.25 in the pre-business core courses and a minimum GPA of 2.0 when they attain junior standing in order to enroll in upper-division business courses.

38 The low probabilities for MATHS 165 students remains puzzling and runs counter to the argument presented in the text. Since this category includes only 5 students, we regard this result as anomalous rather than a disconfirmation of our general analysis.

39 There is some anecdotal evidence for this conjecture. The requirement that students must earn a minimum grade of C in MATHS 135 was enforced beginning in the Fall 2006 semester, after it had been published in the 2006–8 university catalog and, thus, became official policy. However, pre-business students were informed that this standard would be “unofficially” applied (with a few exceptions) starting in Fall 2005. Table 6 shows that only 9.5 percent of the MATH 135 students earned a grade of D before taking ECON 221, compared to 15.2 and 17 percent of the MATHS 131 and 132 students, respectively. Moreover, about 11 percent of MATHS 161 students earned a D grade before taking ECON 221.

40 Yang and Raeshler (2005), p. 6 comment that: “As is well known in the literature, SAT is a good predictor for freshmen, and its explanatory power wears off as students become sophomores and so on.” ECON 221 students are typically either second-semester sophomores or juniors.

41 Hoag and Benedict (2007), p. 15.

42 Ibid.

43 Our university requires that researchers using student records must obtain explicit written permission from students if they can be identified from the data used. Accordingly, they provided the data we requested in a format that excluded student identities (e.g., names, student IDs, course section numbers, etc.).

44 Because our data set ended in Summer 2006, we are unable to directly examine the impact of this math grade requirement on student performance in the business statistics course. However, footnote 38 contains some anecdotal evidence on its effect.