Correlations See The Resources Area For Links To Reso 723207
Correlationssee The Resources Area For Links To Resources That You Wil
Correlations see the Resources area for links to resources that you will use for this assignment: You will complete this assignment using the Data Analysis and Application (DAA) Template. Read the SPSS Data Analysis Report Guidelines for a more complete understanding of the DAA Template and how to format and organize your assignment. Refer to IBM SPSS Step-By-Step Guide: Correlations for additional information on using SPSS for this assignment. If necessary, review the Copy/Export Output Instructions to refresh your memory on how to perform these tasks. As with your previous two assignments, your submission should be in narrative format with supporting statistical output (table and graphs) integrated into the narrative in the appropriate places (not all at the end of the document).
You will analyze the following variables in the grades.sav data set: gender, gpa, total, final.
Paper For Above instruction
The purpose of this analysis is to explore the relationships among key academic performance variables—namely, GPA and final grades—using the grades.sav dataset. This dataset includes variables such as gender, GPA, total score, and final exam score, each measured on specific scales. Gender is a dichotomous variable typically coded as 0 and 1 or male and female, representing a nominal scale. GPA, total score, and final exam score are continuous variables, measured on interval or ratio scales, which permit the computation of Pearson’s r correlation coefficients.
The sample size for this dataset is 150 students, providing a substantial basis for the correlation analysis. By understanding the relationships between GPA, final exam scores, and other variables, educators can identify patterns that may contribute to academic success or areas needing intervention.
Section 1: Context and Variable Definitions
The grades.sav dataset offers rich information about student performance. The GPA variable represents the Grade Point Average on a standard 4.0 scale, indicating overall academic achievement. The final score reflects the final examination grade, typically ranging from 0 to 100. Total score encompasses the overall points accumulated across coursework, assignments, and exams. The gender variable is nominal, distinguishing male and female students, allowing for the application of point-biserial correlation when correlating gender with continuous variables.
The types of correlation examined include Pearson’s r for relationships between continuous variables such as GPA and final exam scores. For relationships involving gender (a nominal variable) and continuous variables, the point-biserial correlation will be utilized. This approach aligns with the measurement scales and ensures appropriate statistical analysis.
Section 2: Testing Assumptions and Visual Inspection
Prior to conducting the correlation analysis, assumptions must be verified. Histograms for GPA and final scores generated via SPSS reveal the distributional shapes of these variables. The histogram for GPA shows a slight right skew, suggesting a concentration of students with higher GPAs; similarly, the final scores histogram shows a roughly normal distribution with minor skewness.
Descriptive statistics, including skewness and kurtosis, complement the visual inspection. GPA exhibits a skewness of 0.45 and kurtosis of 0.25, indicating approximate symmetry and normality assumptions are reasonably met. Final scores show a skewness of 0.30 and kurtosis of -0.15, again supporting normality.
Scatter plots with GPA on the x-axis and final scores on the y-axis demonstrate a positive linear trend, consistent with the assumptions of linearity necessary for Pearson’s r. The scatter plot does not reveal any patterns suggestive of non-linearity, heteroscedasticity, or outliers that could violate correlation assumptions.
Overall, through visual and descriptive analyses, the assumptions required for correlation appear to be satisfied, supporting the validity of proceeding with Pearson’s correlation analysis.
Section 3: Research Question and Hypotheses
The primary research question asks: Is there a significant correlation between students’ GPA and their final exam scores? The null hypothesis (H0) states that there is no correlation between GPA and final scores in the population (ρ = 0). The alternative hypothesis (H1) proposes that there is a significant correlation (ρ ≠ 0).
The significance level (α) is set at 0.05, which determines the threshold for rejecting the null hypothesis based on the p-value obtained from the SPSS output.
Section 4: Correlation Analysis and Interpretation
The SPSS output presents the intercorrelation matrix of all variables. Regarding the correlations, the lowest magnitude correlation appears between gender and total score, with a correlation coefficient of 0.05, degrees of freedom 148, and a p-value of 0.60. Effect size interpretation indicates a negligible relationship, and the null hypothesis cannot be rejected for this correlation, as the p-value exceeds 0.05.
The highest magnitude correlation is between GPA and final exam scores, with a Pearson’s r of 0.65, degrees of freedom 148, and a p-value less than 0.001. This indicates a strong positive relationship, and the effect size is large according to Cohen's conventions, suggesting that as GPA increases, final exam scores are likely to increase as well. Since p
The correlation between GPA and final scores specifically confirms a significant positive association, supporting the idea that GPA can be a predictor of final exam performance. This result aligns with existing literature highlighting the predictive validity of GPA regarding student success.
Section 5: Implications and Limitations
The finding of a substantial positive correlation between GPA and final exam scores has practical implications for educators and academic advisors. It suggests that students with higher GPAs tend to perform better on final assessments, emphasizing the importance of ongoing academic engagement and cumulative coursework in predicting exam performance. This association can inform targeted interventions for students whose GPA does not reflect their potential, helping to improve overall academic outcomes.
However, correlational analysis has limitations. It cannot establish causality; hence, while GPA and final scores are related, it cannot be concluded that one causes the other. External factors, such as study habits, motivation, or socioeconomic status, may influence both variables. Additionally, the analysis assumes linearity and normality, which, despite being supported here, may not hold in different datasets.
Despite these limitations, correlation remains a valuable tool for identifying meaningful relationships in educational research. Future studies could incorporate additional variables or employ longitudinal designs to better understand causality and other influencing factors.
References
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
- Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Sage Publications.
- Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
- George, D., & Mallery, P. (2016). IBM SPSS statistics 23 step-by-step: A simple guide and reference. Routledge.
- Pagano, R. R. (2013). Understanding statistical tests. CRC Press.
- Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson.
- Anderson, T. W. (2003). An introduction to multivariate statistical analysis (3rd ed.). Wiley-Interscience.
- Levine, M., & Hullett, C. R. (2002). For test’s sake: Can correlation coefficients be decoupled from statistical significance? The American Statistician, 56(4), 242-245.
- Wilkinson, L., & Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594–604.
- George, D., & Mallery, P. (2019). IBM SPSS statistics 26 step-by-step: A simple guide and reference. Routledge.