Basic Math Skills and Performance in an Introductory Statistics Course

Abstract

We identify the student characteristics most associated with success in an introductory business statistics class, placing special focus on the relationship between student math skills and course performance, as measured by student grade in the course. To determine which math skills are important for student success, we examine (1) whether the student has taken calculus or business calculus, (2) whether the student has been required to take remedial mathematics, (3) the student's score on a test of very basic mathematical concepts, (4) student scores on the mathematics portion of the ACT exam, and (5) science/reasoning portion of the ACT exam. The score on the science portion of the ACT exam and the math-quiz score are significantly related to performance in an introductory statistics course, as are student GPA and gender. This result is robust across course formats and instructors. These results have implications for curriculum development, course content, and course prerequisites.

• Determinants of student performance
• Introductory collegiate statistics
• Mathematical skills

Acknowledgements

We would like to thank Ryan Haley and Denise Robson for their participation and assistance, and Kevin McGee for his insightful comments. We would also like to thank the University of Wisconsin Oshkosh for support through a Scholarship of Teaching and Learning Grant.

End Notes

1. Formal IRB approval was granted for this study. Appropriate records are on file with the university and can be provided upon request. In addition, students were provided with information sheets and consent forms to indicate their agreement to participate in the study, as well as to our retrieval of their official GPA and ACT scores from the university. Only three of the students who completed the course refused to give consent.

2. Consistent with Maxwell and Lopus (1994), we find that students tend to overstate their GPA and ACT scores. Students overstate their GPA, compared to official university records, by an average of 0.05. Similarly, students overstate their composite ACT score by 5 (out of 36). Both results are statistically significant.

3. The math quiz was originally developed for introductory economics, based on years of teaching. The particular math concepts covered by the quiz are similar to those reviewed in introductory statistics textbooks, as well as questions on our university's math placement exam for incoming freshmen. Tests of reliability indicate that none of the questions should be eliminated.

4. In terms of our estimated regression results, we argue that the selection bias is not a problem. Consider an equation determining attendance with an error u. This equation can be represented as: where is the constant and is the vector (j) of coefficients on the exogenous variables x_j for all observations, i, including the math variables such as math quiz score. We argue that the error u is positively correlated with the error e in the grade equation that specifies that student i's grade depends on a vector (j) of explanatory variables (z): . In this regression equation, is the constant and is the vector of coefficients on the exogenous variables z_j for all observations i. This type of relationship between the error terms would suggest that students who are more likely to attend class are also more likely to get higher grades and have correspondingly better math skills. This expected value of the error is like an omitted variable in the grade determination equation. So when the regression is run, this negative correlation between math variables and the expected e would cause the coefficients on the math variables to be underestimated (see Ballard and Johnson 2004 for further details).

5. We also check for multicollinearity between the various math and academic variables and between the math variables and race and gender. We find little evidence that multicollinearity is a problem examining correlation coefficients. In addition, we compare regressions, dropping one of the math variables and then looking at the effect on the t-statistics of the remaining variables; we find no significant changes.

6. We include a math-squared term in these regressions, and the evidence from the regressions suggests that the relationship between student performance in the class and the math quiz is not expressed better as a quadratic.

7. Ordered probit analysis does not allow the computation of a straight-forward R-squared value. The adjusted R-squared reported here is one that is simulated, and the usefulness of these simulated values is the subject of much discussion. Perhaps a more clear proximate measure would be the R-squared value from a standard OLS regression, with grade as the dependent variable and including the same explanatory variables. In doing so, we find an R-squared of 0.4277. In either case, a small R-squared value only implies that the variance of the error is large relative to the variance in the dependent variable. Thus it may be difficult to precisely estimate ; however, larger sample sizes can allow us to estimate the partial effects precisely, even with many unobservable factors unconsidered. Therefore, while we may be explaining only a fraction of the total variance in statistics grades with these explanatory variables, we can still be confident that our estimated coefficients on the explanatory variables are accurate.

8. We attempted to enter the “hours worked per week” variable in a number of different ways because the variable has skewed distribution. However, none of the categorical variables (work versus do not work; work less than 10 hours a week, work more; work less than 20 hours a week, work more) we tried generated significant results. We also considered that “work” may enter in a non-linear form, and thus included both “work” and “work-squared,” but with no impact on the general results of the model.

9. Cronbach's Alpha is calculated as the square of the correlation between the measured scale and the underlying factor; generally alpha values of 0.70 or higher are considered acceptable. However, our scale is an imperfect yardstick for judging the reliability of the math quiz score as it includes items related to student intelligence or effort such as GPA, but that is not necessarily related to math skills, and thus we argue that a value of 0.669 is sufficiently indicative of the math quiz scores' reliability. Another way to identify this is by looking at the without item-test correlation. For well-fitting items, the alpha decreases when you shorten the test list. Removing math quiz score from the list of items reduces Cronbach's alpha from 0.6686 to 0.6161.