Multi-Semester Comparison of Student Performance Using One-Way ANOVA

Multi-Semester Comparison of Student Performance Using One-Way ANOVA
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One-Way ANOVA
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Abstract
The performance of students is the most crucial metric used to measure the quality of any learning institution and the different factors that influence it. Institutions of learning invest a lot of resources to understand these factors to improve and maintain the high performance of students in their schools. This study focuses on understanding one aspect that is believed to influence the students' performance and is vital in predicting students’ future performance. The research attempts to find out if students’ performance varies between semesters. The data used in this research has been obtained from Kaggle and was cleaned and transformed before being analyzed. SPSS version 25 was used to perform analysis for the descriptive statistics, graphs, and inferential statistics. A one-way ANOVA analysis and pairwise comparison were performed to provide inferential statistics to answer the objective and hypothesis of this study. The finding of the research showed that there was a significant variation in mean CGPA, and students seem to perform their best in their fifth semester and their worst in the third semester. These results show that students’ performance does vary, and the performance becomes better in the final semester of study.
Introduction
Various factors influence the performance of a student in higher institutions of learning. Different studies have been abshownome of these factors may vary from one population to another. In a study done by Getahun (2022), it was revealed that age, gender, hours of study, family monthly income, and teacher satisfaction were some of the notable significant factors that influenced the performance of students in Bahir Dar Polytechnic College. In as much as some other factors are universally accepted to impact the performance of a student, some might vary from region to region. According to Abu Saa et al. (2019), some factors include students’ demographics, social information, e-learning activities, class performance, and previous grades.
Students’ performance in any institution is important, and understanding the elements that influence it is vital. This is the case because the most crucial metric used to measure the quality of any learning institution is the students’ performance. Many learning institutions are inventing immensely in developing models that can predict their students’ performance. This study uses data from Kaggle to establish if there is a significant difference in the CGPA of the students across five different semesters.
Study Objective
The purpose of this study is to establish if there is a significant difference in the mean CGPA scores of sampled students between their first and fifth semesters. This objective will be achieved by performing an ANOVA analysis coupled with a pairwise comparison of the CGPA scores across the five semesters. This analysis will help establish if the CGPA varies between semesters and which pair of semesters have significant mean differences in their CGPA. The hypotheses for this study are:
H0:There is no signficant mean difference in the CGPA score by semester
H1:There is a signficant mean difference in the CGPA score by semester
Methods
The data used in this study was obtained from the Kaggle website and it consisted of 179 sampled students. The dataset contained the CGPA of the sampled students saved in a wide format. After getting rid of 10 cases with missing values in the dataset, a transformation was done on the data to change it from the wide format to the long format to prepare it for analysis in the SPSS software Version 25. The analysis started by generating descriptive statistics such as the mean, median, and standard deviation of the score and plotting its histogram and boxplot. Using the boxplot, outliers in the dataset were located and removed. The outputs for this analysis can be found in the appendix of this document. Afterward, a one-way ANOVA analysis and pairwise comparison were performed to provide inferential statistics to answer the objective and hypothesis of this study. Similarly, the results of the inferential analysis have been shared in the appendix of this document.
Results and Discussion
In the analysis, the descriptive statistics of the CGPA were computed depending on the semester. The semester with the highest CGPA score on average was the fifth (M=7.47, SD=1.02), followed by the first semester (M=7.09, SD=0.79), then the fourth semester (M=7.05, SD=1.04), then the second semester (M=6.96, SD=0.85) and lastly the third semester (M=6.64, SD=0.92). The descriptive statistics above provide an impression of what might be expected after further analyzing the data. Figure 2 in the appendix is a boxplot that shows the distribution of the CGPA for the students across the different semesters. This output helps visually understand the variation in the scores in the various semesters, and the scores of the third semester are seen to be significantly different from the rest of the semesters. However, the boxplot cannot be used to provide conclusive results about the presence of a significant variation between the semesters.
On performing a one-way ANOVA analysis of the data, Table 2 in the appendix was generated. The results of this analysis show that there was a significant difference in CGPA score across the semesters, F (4, 829) = 13.96, p<0.05. This implies that at least one semester has a mean CGPA score that is significantly different from the rest. To investigate further which pair of semesters significantly varied for each other, a Turkey HSD was performed, and the results are shared in Table 3 of the Appendix.
The pairwise comparison table shows that the mean CGPA of the sampled students in their first semester significantly varied from the third and fifth semesters. However, the first semester's mean CGPA was statistically similar to that of the second and the fourth year. The mean CGPA of the second semester was obtained to be significantly different from that of the fourth semester only but statistically the same as that of the other semesters. The third semester was obtained with a mean CGPA that varied from the rest of the semesters except the second semester. The Fourth semester had a significantly different mean CGPA from the third and the fifth and not the first and the second. The fifth semester’s mean CGPA varied from all the other semesters.
Based on the obtained results, it is evident that students’ results are influenced by their semester. Students have been found to perform averagely well in their first semester. The performance then drops in the consecutive semesters to hit its lowest in the third semester. Afterward, the CGPA scores start to improve in the fourth semester and hit an all-time high in the fifth semester. This trend might indicate significant factors that cause the students’ performance to decrease steadily from their first semester of entry to their third. One of the factors might be the social changes that these students face as they try to fit into the new environment. Suddenly, the wheels turn when the students reach their fourth semester.
Conclusion
The findings of this research have been able to answer the objection that this study had set out to uncover. The study was interested in finding out if the CGPA score of students does vary significantly depending on the semester the students were in. The results of the analysis show that the variations exist, and the fifth semester seemed to differ substantially from the rest. The students performed significantly better in their fifth semester than in other semesters. Also, the findings show that the students performed worse on average in their third semester.
References
Abu Saa, A., Al-Emran, M., & Shaalan, K. (2019). Factors affecting students’ performance in higher education: a systematic review of predictive data mining techniques. Technology, Knowledge and Learning, 24(4), 567-598.
Getahun, K. A. (2022). A Bayesian Approach to Investigating Factors Influencing Polytechnic College Students’ Academic Achievement. Education Research International, 2022.
Appendix
Figure SEQ Figure \* ARABIC 1: The histogram for the CGPA of the students
Figure SEQ Figure \* ARABIC 2: The boxplot of the CGPA by semester
Table SEQ Table \* ARABIC 1: Descriptive statistics of the CGPA scores by semester

semester

Statistic

Std. Error

cgpa

First Semester

Mean

7.0901

.06095



95% Confidence Interval for Mean

Lower Bound

6.9697





Upper Bound

7.2104




5% Trimmed Mean

7.0879




Median

7.1100




Variance

.628




Std. Deviation

.79239




Minimum

5.11




Maximum

9.15




Range

4.04




Interquartile Range

1.15




Skewness

.073

.187



Kurtosis

-.209

.371


Second Semester

Mean

6.9802

.06401



95% Confidence Interval for Mean

Lower Bound

6.8538





Upper Bound

7.1066




5% Trimmed Mean

6.9633




Median

6.8200




Variance

.688




Std. Deviation

.82973




Minimum

5.48




Maximum

9.21




Range

3.73




Interquartile Range

1.27




Skewness

.287

.187



Kurtosis

-.628

.373


Third Semester