Foundations of Non-Parametric Statistical Inference

When your data does not fit the clean, bell-shaped curves of classical statistics, standard parametric tests can lead to incorrect conclusions. Non-parametric statistical inference provides the vital tools you need to analyze real-world data without making rigid assumptions about its underlying distribution. This text-based course guides you from foundational probability concepts to executing and interpreting essential non-parametric tests. You will transition from calculating basic rank-based statistics to confidently selecting and applying the right distribution-free test for any dataset. Through clear explanations and written step-by-step calculations, you will learn how to handle ordinal data, small sample sizes, and skewed distributions common in modern data analysis. What you'll learn: - Understand the core differences between parametric and non-parametric statistical frameworks. - Apply sign tests and signed-rank tests for single samples and paired observations. - Compare independent groups using the Mann-Whitney U test and Kruskal-Wallis test. - Measure non-linear associations using Spearman's rank correlation and Kendall's tau. - Evaluate goodness-of-fit and sample distributions using the Kolmogorov-Smirnov test. - Practice selecting the appropriate statistical test based on data type, sample size, and research design. The course begins with foundational definitions, explaining why and when to choose non-parametric methods over parametric ones. Next, you will progress systematically through one-sample, two-sample, and multi-sample tests, concluding with practical guidelines on correlation and goodness-of-fit analysis. This course is designed for beginners, students, and data professionals who have a basic understanding of introductory statistics but no prior experience with non-parametric methods. Start reading today to unlock flexible, robust techniques for analyzing any dataset.