Chapter 14: Statistical Process Control

Nonparametric tests prove invaluable when working with ordinal or ranked data, when sample sizes are small, or when the underlying population distributions deviate significantly from normality. The chapter establishes the conceptual foundation by contrasting parametric and nonparametric methods, emphasizing that while nonparametric tests sacrifice some statistical power, they gain flexibility and applicability across diverse data types. The sign test represents one of the simplest nonparametric approaches for analyzing matched pairs by converting differences into positive or negative indicators and counting their frequencies. The Wilcoxon signed-rank test extends this logic by incorporating magnitude information through ranking, making it more powerful while remaining distribution-free. For independent samples, the Mann-Whitney U test provides a nonparametric alternative to the independent samples t-test, using rank sums to determine whether two groups differ significantly. When comparing three or more independent groups, the Kruskal-Wallis test extends the logic of rank-based comparisons across multiple samples simultaneously. Beyond hypothesis testing, the Spearman rank correlation coefficient offers a nonparametric measure of association between two variables, detecting monotonic relationships without assuming linearity or normal distributions. Throughout the chapter, systematic procedures guide students through test calculations, decision-making criteria, and software implementation. Real-world applications demonstrate how these methods address research questions in psychology, medicine, business, and other fields where traditional parametric assumptions cannot be reliably met. By mastering these techniques, students develop the analytical flexibility to handle complex datasets and choose appropriate methods based on data characteristics rather than forcing data into restrictive statistical frameworks.