Evaluating Student Statistics Performance Using SAS®/STAT Procedures

Seid M. Zekavat, Loyola Marymount University of Los Angeles Kathryn Wilson, Loyola Marymount University of Los Angeles

ABSTRACT The purpose of this study is twofold. First, it intends to determine whether or not gender affects student performance in Business and Economics Statistics. Second, it investigates whether or not class attendance and completing regular homework assignments in an introductory statistics course have any bearing on student final semester grades. Statistical tools used in this study include regression analysis, F and Z tests of null hypotheses, the difference between two population means test and pie charts. Preliminary findings suggest that completion of homework assignments holds a significant relation to the semester scores. The relationship between class attendance and semester scores, however, seems less significant than that of homework. As expected, the female students performed better than their male counterparts. Females consistently earned a higher percentage of A’s and B’s. INTRODUCTION In recent years, institutions of higher learning have taken serious steps to develop and improve students’ capability in quantitative analysis and research. For the last eleven years some 90 institutions in Southern California participated in the Southern California Conference on Undergraduate Research (SCCUR), where about a thousand students and their faculty mentors participate in the Conference. At Loyola Marymount University of Los Angeles, for example, students of undergraduate Statistics and Economics are taught to

employ statistical concepts and tools in mini-research cases. SAS®

and other Statistics software facilitate the research and make their efforts rewarding. What makes this study unique is the common presumption that female is not as quantitatively oriented as male. In fact, this false perception has, for a long time, instilled in females’ minds that they are no match to the males’ quantitative ability. Data The authors took a random sample of 216 final exam scores, and corresponding completed homework assignments and classroom attendance from the records of a large number of students who had taken the same introductory statistics course within the past several years. The data was organized into 108 male and 108 female to conduct multiple regression analyses and the difference between two-means hypotheses. For the purpose of presenting an overall summary, the data was also grouped into the five letter grades of F’s, D’s, C’s, B’s, and A’s respectively. Statistical Methodology A linear multiple regression equation used in this study for female and male students may be expressed as:

yi = b0 + b1 x1 + b2 x2 + ui,

where, yi represents the final semester scores as a dependent variable, x1 is handed-in homework and x2 attendance, as independent variables and ui is error term or residual. An F test of hypothesis is conducted at the .05 level of significance to determine if students’ attendance and homework have significant bearings on the average semester scores. For the second approach, pie charts of the five latter grades earned by the two groups are compared. In order to see if the differences exhibited in the pie charts are also a manifest in the population from which the sample of 180 was taken, a right-tailed test of hypothesis about the difference between the population average scores of the two genders is conducted. The null hypothesis contends that there is no difference between the population average scores of the two genders and the alternative hypotheses indicates that the population average score of female students is higher. In order to determine the effect of attendance and assignment separately on final scores simple linear regressions are developed for each gender.

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Findings The results of the multiple regression analysis indicate that for both male and female, homework has a significant positive relationship with the average semester grades. The relationship between attendance and scores does not seem to be strong. One reason for this insignificant relationship is that most students who miss class for any reason utilize the textbook and borrowed class notes to prepare for the exam. This is particularly true when the instructor explicates in his review the type of questions he would include in the exam. Table 1 shows the ANOVA table for the multiple regression analysis.

ANOVA TABLE

Regression Analysis of Final Score versus Assignments, Classes Attendance

Final Score = 25.5 + 0.814 Assignments Turned In + 1.76 Classes Attended

Predictor Coef SE Coef T P

Constant 25.468 7.430 3.43 0.001 Assignments Turned In 0.8145 0.5642 1.44 0.152 Classes Attended 1.7558 0.4662 3.77 0.000

S = 15.8326 R-Sq = 39.1% R-Sq (adj) = 38.0%

Analysis of Variance

Source DF SS MS F P Regression 2 16912.2 8456.1 33.73 0.000 Residual 105 26320.6 250.7 Total 107 43232.8

The graphs of surface plots for the multiple regression obtained above are shown in Figures 1 and 2. Figure 1 Figure 2

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Final Score

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Surface Plot for MalesFinal Score with Classes Attended and Assignments Turned In

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Surface Plot for FemalesFinal Score with Classes Attended and Assignments Turned In

These graphs indicate positive relationships between the response y (average semester scores and homework and attendance). Referring to the multiple regression results, the coefficients of x1 and x2 indicate that for every assignment turned in, the average score increases by 0.814 points and for every class attended the score is improved by an average 1.6 points.

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The critical value of F for the 5% level of significant is 3.09, which is less than 33.73, the F value obtained from the ANOVA table above. Thus, the null hypothesis of no overall relationship between the final semester scores and the variables of attendance and assignment is rejected. The test of hypothesis about the difference between the mean of the two populations gives similar results. A strong z value of 17.93 is far greater that the critical z value of 1.96 at the 5% level of significance. Therefore, the null hypothesis of no difference between the means of the two population scores earned by the two genders is rejected. In other words, the overall females’ performances in introductory statistics are superior to those of the males. Figures 3 and 4 are graphs of the simple linear regressions showing the impact of attendance and assignment on final semester scores for both genders.

Figure 3

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S 15.9134R-Sq 37.9%R-Sq(adj) 37.3%

MALE- Final Score vs Classes AttendedFinal Score = 21.02 + 2.290 Classes Attended

Assignments Turned In

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S 16.7886R-Sq 30.9%R-Sq(adj) 30.2%

Male Final Scores with Assignments Turned InFinal Score = 49.76 + 2.502 Assignments Turned In

Figure 4

Classes Attended

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S 11.3162R-Sq 21.8%R-Sq(adj) 21.1%

Female Final Scores with Classes AttendedFinal Score = 40.16 + 1.701 Classes Attended

Assignments Turned In

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S 11.9416R-Sq 12.9%R-Sq(adj) 12.1%

Female Final Scores with Assignments Turned InFinal Score = 63.78 + 1.477 Assignments Turned In

With respect to the semester letter grades earned by the two genders, the females have predominantly more A’s and B’s than the males. To demonstrate this, pie charts of the percentages of letter grades for both genders are shown in Figures 5 and 6.

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Figure 5

A (26, 24.1%)

D (11, 10.2%)

F ( 8, 7.4%)

C (21, 19.4%)

B (42, 38.9%)

Male Student Letter Grades Percentages

Figure 6

A (37, 34.3%)

F ( 2, 1.9%)D ( 1, 0.9%)

C (18, 16.7%)

B (50, 46.3%)

Female Student Letter Grades Percentages

Conclusion Do males have lower aptitudes in quantitative analysis in comparison with females? When we put this question to the females, they stressed the belief that in general one gender is not smarter than the other. The level of performance, they indicated, depends on how much students apply themselves in learning and preparation for tests. Basically, females are more serious and studious. Some replied that females are more competitive and try to make a point. This study shows that in general both attendance and completing assignments does make a difference in the level of final semester grades. Assignments completed, however, have a greater impact of the final grades. The study also made it clear that high academic performance is not the monopoly of males. Whatever the reason, in the sphere of Introductory Business Statistics the females overall performance is superior to that of males. COPYRIGHT INFORMATION

SAS is a registered trademark of SAS Institute, Inc. in the USA and other countries. ® Indicates USA registration. Other brand or product names are registered trademarks or trademarks of their respective companies.

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CONTACT INFORMATION Seid M. Zekavat, Ph.D. Loyola Marymount University Los Angeles, California 90045 Work Phone: (310) 338-7372 Fax: (310) 338-1950 E-mail: szekavat@lmu.edu Web: www.perilsofblindfaith.com

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