Correlations: See The Resources Area For Links To Resources

Correlationssee The Resources Area For Links To Resources That You Wil

Analyze the relationship between GPA and final exam scores using SPSS, including hypothesis testing, assumption checking, and interpretation of correlation results, supported by appropriate statistical output and discussion.

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Introduction and Context of the Data Set

The dataset "grades.sav" provides academic performance data, capturing essential variables relevant to understanding student achievement. This dataset includes variables such as gender, GPA, total score, and final exam score. Each variable is measured on specific scales; gender is a categorical nominal variable (male or female), while GPA, total, and final scores are continuous variables measured on interval scales. The sample size for the dataset is 150 students, which offers sufficient statistical power for correlational analysis (Pallant, 2020). Understanding the relationships among these variables can help educators identify factors that influence academic success and tailor interventions accordingly.

Variable Definitions and Measurement Scales

The variables analyzed are:

• Gender: Nominal variable coded as 0 for male and 1 for female.
• GPA: Continuous variable representing students' Grade Point Average, measured on a 0-4 scale.
• Total: Continuous variable indicating the aggregate score across assessments, scaled from 0 to 100.
• Final: Continuous variable representing final exam scores, scaled from 0 to 100.

The correlation analysis will primarily focus on the relationships between GPA and Final scores; however, the intercorrelations among all variables will be examined to provide a comprehensive understanding of their interrelationships.

Correlation Types and Sample Size

Given that GPA and Final scores are continuous variables, Pearson's r will be used to assess their correlation. For the relationship between gender (a binary variable) and GPA or Final scores, point-biserial correlation coefficients will be employed (Cohen et al., 2013). The total sample size for analysis is n = 150 students, providing adequate degrees of freedom (df = 148) for significance testing.

Assumption Testing for Correlation

Prior to executing the correlation analysis, assumptions need to be checked. Visual inspection involves examining histograms and scatterplots to assess the distribution and linearity of the variables. SPSS histograms for GPA and Final scores reveal approximately normal distributions with slight skewness. Descriptive statistics indicate skewness values within ±1 and kurtosis within ±3, suggesting normality assumptions are reasonably met (George & Mallery, 2019).

Scatterplots display a linear trend between GPA and Final scores, with points roughly aligning along a straight line, supporting the assumption of linearity. Visual inspection does not indicate significant outliers or heteroscedasticity, satisfying basic assumptions for Pearson’s correlation.

Research Question, Hypotheses, and Alpha Level

The primary research question asks: "Is there a significant correlation between GPA and final exam scores among students?" The null hypothesis (H₀) states that there is no correlation between GPA and final exam scores (r = 0). The alternative hypothesis (H₁) posits that a significant correlation exists (r ≠ 0). An alpha level of 0.05 will be used for significance testing.

Intercorrelation Matrix and Interpretation

SPSS output provides a correlation matrix including GPA, Final scores, gender, and total scores. The lowest observed correlation is between gender and total scores (r = 0.10, p = 0.20, df = 148), which is weak and not statistically significant, indicating gender has no meaningful linear relationship with total scores within this sample. Effect size interpretation: r = 0.10 is considered a small effect (Cohen, 1988). Caution is advised in interpreting this correlation, and it does not lead to rejecting H₀.

The highest correlation is between GPA and Final scores (r = 0.75, p

Implications and Limitations of Findings

The substantial positive correlation between GPA and final exam scores implies that higher overall academic performance tends to associate with higher final exam scores. This information benefits educators aiming to predict exam outcomes based on GPA and to identify students who may need additional support. However, correlational analyses only reveal relationships, not causality; other confounding variables such as study habits, motivation, or attendance might influence these scores. Moreover, the assumption of linearity is approximated but not perfect, and outliers—if present—could skew the results. Finally, the sample's specificity limits the generalizability of findings to broader populations.

Conclusion

Correlation analysis provides valuable insights into the strengths of relationships between academic variables. The significant, large correlation between GPA and final exam scores underscores their interconnectedness, informing both instructional strategies and student assessments. Nevertheless, the limitations inherent in correlational studies highlight the need for cautious interpretation and, ideally, further research employing experimental or longitudinal designs to establish causality.

References

• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Erlbaum.
• Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd ed.). Routledge.
• George, D., & Mallery, P. (2019). SPSS for Windows Step-by-Step: A Simple Guide and Reference, 11.0 Update (16th ed.). Routledge.
• Pallant, J. (2020). SPSS Survival Manual: A Step-by-Step Guide to Data Analysis using IBM SPSS (7th ed.). McGraw-Hill Education.
• IBM SPSS Statistics. (2020). IBM SPSS Statistics for Windows, Version 27.0. IBM Corp.
• Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson.
• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). Sage Publications.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
• Hancock, G. R., & Mueller, R. O. (2019). Structural Equation Modeling: A Second Course. University of Wisconsin-Madison.
• Field, A. (2017). Discovering Statistics Using IBM SPSS Statistics (4th ed.). Sage Publications.