Statistical Modeling & Regression · Non-Parametric Statistics

Non-Parametric Statistics: Comparison of k Independent Samples

Public introduction · full guide in Eikos

Introduction

What this guide covers

The analysis of independent samples constitutes one of the pillars of applied statistics. While parametric Analysis of Variance (ANOVA) requires the validity of the Gaussian assumptions and the constancy of variances across groups, the scientist regularly faces markedly asymmetric data, ordinal scale, or contaminated by severe outliers.

Overview

Topics covered

  • Introduction
  • Inference of k independent samples
  • 1. Parametric limits and the non-parametric alternative
  • 2. Fundamentals of Range Inference
  • The process of mathematical rank assignment
  • 3. The Kruskal-Wallis Test (Complete Theory)

Related concepts

Main connections

  • Non-parametric tests
  • Variance & standard deviation
  • Hypothesis testing
  • Median & robust location
  • Analysis of variance (ANOVA)
  • Multiple testing & FWER/FDR

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

Yij=μ+τi+εij
View LaTeX sourceY_{ij} = \mu + \tau_i + \varepsilon_{ij}