Correlation Analysis

This chapter introduces correlation analysis as a statistical method for evaluating the strength and direction of relationships between two variables in health research. The chapter begins with Pearson’s Product-Moment Correlation, which is appropriate for numerical interval/ratio data when assumptions such as normality, linearity, homoscedasticity, and the absence of extreme outliers are reasonably satisfied. Students learn to calculate and interpret the correlation coefficient (r), which ranges from −1 to +1, and to test its statistical significance using a p-value and confidence interval. The material emphasizes examining correlation visually with scatter plots, as shown in the example relating LDL cholesterol to cardiovascular disease risk.

The chapter then discusses nonparametric correlation methods, particularly Spearman’s Rho and Kendall’s Tau, which are useful when parametric assumptions are not met or when variables are ordinal. Spearman correlation evaluates monotonic relationships by converting observations into ranks, whereas Kendall’s Tau is based on concordant and discordant pairs and is particularly useful for small samples or data containing many tied ranks. The chapter provides health-related examples, including the relationship between anxiety and systolic blood pressure and between pain and mobility among patients with osteoarthritis. Students also learn to implement Pearson, Spearman, and Kendall correlations in R, including hypothesis testing and graphical visualization through scatter plots and trend lines.

Finally, the chapter focuses on interpreting correlation coefficients in a health-data context and emphasizes the critical distinction between statistical significance and practical or clinical significance. Students learn to consider the direction, strength, p-value, confidence interval, and coefficient of determination (R²) when interpreting results. A case study on dietary fiber intake and fasting blood glucose shows how correlation analysis fits into a broader health research workflow, including missing-data handling, data transformation, outlier assessment, selecting an appropriate correlation method, and adjusting for potential confounders. Importantly, the chapter repeatedly stresses that correlation does not imply causation; an observed association may be influenced by confounding variables. Thus, the overall goal is not merely to calculate a correlation coefficient but to enable students to select an appropriate method, analyze health data using statistical software, interpret the findings correctly, and draw appropriately cautious conclusions.