STEVENS MA 331 - Determining Factors of GPA

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Determining Factors of GPA Among full-time undergraduate Stevens students, number of credits and which school a student belongs to were the most important factors in determining GPA. Natalie Arndt Allison Mucha MA 331 12/19/07 We pledge our honor that we have abided by the Stevens Honor System.2Introduction There is much debate surrounding the effects of various factors on a student’s performance in the academic world. Sophisticated studies take in dozens of variables and years’ worth of data in attempt to predict how successful a particular student will be during his or her academic career. Determining which factors most greatly affect academic performance would not only allow individuals to predict future GPAs or grades, but could possibly help students make lifestyle choices that facilitate success. This study aims to deduce which factors most significantly impact a full-time Stevens student’s GPA. Other points of interest included making use of methods and analytic techniques discussed in class, as well as observing any significant differences between engineering and science students at Stevens. The ultimate goal of this study would be to be able to predict a Stevens student’s GPA based on the factors that are determined to be significant. Data Collection Initially, the data being considered was notably less focused than it would become later in the study. Factors such as average hours of non-studious work per week, average hours of sleep per night, or which SAT score was higher for the student in question were proposed. Ultimately, these factors were dropped in favor of variables that did not require loose estimation or guess-work. The list of factors was refined to the following: gender, major, number of semesters at Stevens, credit load per semester, the corresponding GPA for that semester, cumulative number of credits, and cumulative GPA. The data was gathered by reaching out to several subsets of the general student body. These students were sent a survey, and were asked to return it voluntarily with full anonymity. This survey can be seen in Figure 1. Only full-time (at least 12 credits), undergraduate Stevens students were considered in the study. Recent alumni who satisfied these conditions during their time at Stevens were also considered.3 Due to the nature of the study, there were numerous lurking variables that had to be accounted for. These factors include: the influence of extracurricular activities on a student’s performance, changes in curriculum from year to year, personal issues, medical problems, any stressful situation that could impact a student’s ability to work, and differences in professors and grading. Perhaps in a more sophisticated study with a longer duration, an appropriate method for removing these lurking variables could be developed. For example, the study could focus on students with similar extracurricular involvement, or eliminate students who have had medical problems or similar traumas. In favor of receiving the greatest number of usable responses, the survey was not designed to do so. Data Preparation After a three week period, the data collection process was terminated. The completed data table can be viewed in Appendix 1. Combined, 28 students participated in the study, which yielded 154 semester’s worth of data for analysis. Among the participants were 18 males and 10 females, with 19 engineering majors, 8 science majors, and 1 art major. One noteworthy fact was that the breakdown of these categorical variables generally reflected the ratios of the entire Stevens student body, providing a roughly stratified sample. The range of GPA for one semester was 2.317 to 4.000. The number of credits taken in any one semester ranged from 12.0 to 25.5. The number of cumulative credits taken thus far ranged from 33.0 to 177.0. After the data was collected, a number of measures were taken to make it easier to manipulate and analyze. All students’ names were removed from the corresponding data, and replaced with an identification number ranging from 1 to 28. Cumulative data was entered as semester number zero, to distinguish it from individual semesters. The students’ primary majors were used to create the “school” category, taking one of the two values “engineering” or “science.” Art majors were not represented significantly enough to be considered in the study. The number of credits per semester was used to create the category referred to as “load.” Beginning with 12 credits and increasing in4increments of 3 (the equivalent of one Stevens class), load categories A through E were thus created. Data Analysis A primary analysis was performed to determine the normality of the data that had been collected. As evidenced by Figure 2a, the distribution of the number of credits per semester was fairly normal, with a slight tail to the right. Figure 2b shows that the normal Q-Q plot is strongly linear. The distribution of GPA, however, was not as regular. Figure 3a shows a strongly skewed distribution with a notable left tail. The normal Q-Q plot shown in Figure 3b does not suggest linearity, implying that the distribution of GPA is not normal for the data collected. The GPA by semester data was combined, and a linear regression performed. The data with the fitted regression line can be seen in Figure 4. The slope of the line is 0.01799, or approximately 0.02, which is statistically significant and meaningful in a school where GPAs are carried out to three decimal places. Unfortunately, the R2 value for this regression was only 0.01623, showing the need for further analysis and the search for a better fitting model. The cumulative GPA data was then combined and fitted with its own linear regression, together seen in Figure 5. The slope of this line was statistically zero, with an R2 value of less than 0.001. As such, this data was no longer considered, as a zero slope implies no relation between cumulative credits taken and cumulative GPA. Residual plots of the GPA by semester data were then considered. The residuals did appear to be centered about zero, with apparent random scatter about that center, as seen in Figure 6a. However, the displacements above and below the zero line were not equal, meaning the data was not normally distributed, and that the relationship between the explanatory and response variables was not necessarily


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