Parametric and Nonparametric Statistics

This chapter introduces parametric and nonparametric statistics as two complementary approaches for analyzing health data. Parametric methods rely on assumptions about the underlying distribution of the data and typically use population parameters such as the mean and variance, whereas nonparametric methods make fewer distributional assumptions and often work with ranks or frequencies. The chapter emphasizes that selecting the appropriate method is important in health research because an inappropriate statistical test can produce biased or invalid conclusions. Students are therefore expected to understand the characteristics, advantages, limitations, and appropriate applications of both approaches.

A major focus is assessing assumptions before applying parametric tests. The chapter discusses normality and homogeneity of variance as key considerations, introducing statistical and graphical approaches such as the Shapiro–Wilk test, Kolmogorov–Smirnov test, Q-Q plot, histogram, Levene’s test, and boxplot. Students are guided to connect these diagnostic results with the selection of an appropriate analytical method. For example, the chapter demonstrates how a study comparing LDL cholesterol across three diet groups can proceed from normality and variance-homogeneity testing to either ANOVA when assumptions are appropriate or Kruskal–Wallis when they are not.

The chapter then develops students’ ability to select and interpret statistical methods based on the characteristics of health data. Nonparametric methods are particularly emphasized for ordinal data, small samples, non-normal distributions, unequal variances, and data containing extreme outliers. Examples include Wilcoxon signed-rank, Mann–Whitney, Chi-square, Kaplan–Meier, and Log-rank analyses. Several health-research case studies are provided, including patient satisfaction, survival data, smoking and COPD, and intervention effects on stress, with R syntax and visualizations to demonstrate practical implementation. Overall, the chapter aims to move students beyond simply knowing statistical tests toward making a logical decision about which method is appropriate, why it is appropriate, how to implement it, and how to interpret the resulting evidence in a health research context. The course material: click the link here