Chi-Square Test Course

Lesson 1 • The Chi-Square Distribution Explained

Derives the chi-square distribution from squared standard normals and explains its shape. Connects distribution properties to practical test interpretation.

Lesson 2 • Assumptions and Validity Conditions

Identifies the conditions required for valid chi-square results, including sample size and independence. Learners learn to verify assumptions before running any test.

Lesson 3 • Probability and Statistical Inference Basics

Covers probability distributions, sampling, and hypothesis logic as prerequisites. Establishes the inferential framework chi-square tests operate within.

Lesson 1 • Applied Goodness-of-Fit Examples

Applies the test to realistic datasets across multiple domains. Builds fluency by exposing learners to varied data structures and null hypotheses.

Lesson 2 • Conceptual Logic of Goodness-of-Fit

Explains how the test measures discrepancy between observed and expected frequencies. Anchors the formula in the distributional foundations from Chapter 1.

Lesson 3 • Interpreting and Reporting Results

Covers how to communicate goodness-of-fit findings clearly and accurately. Addresses effect size and practical significance alongside statistical significance.

Lesson 4 • Specifying the Null Distribution

Teaches how to define the theoretical distribution under the null hypothesis. Covers uniform, known-proportion, and model-derived distributions.

Lesson 1 • Independence vs. Association in Data

Defines statistical independence and contrasts it with association in categorical data. Sets the conceptual foundation for the independence test.

Lesson 2 • Building and Reading Contingency Tables

Teaches construction of two-way tables from raw data and how to read row, column, and cell values. Directly prepares learners for expected frequency computation.

Lesson 3 • Measuring Strength of Association

Introduces measures that quantify how strongly two variables are associated beyond significance. Connects statistical results to practical meaning.

Lesson 4 • Executing the Independence Test

Guides learners through the full test procedure for two-way tables. Covers degrees of freedom calculation specific to contingency table dimensions.

Lesson 1 • Post-Hoc Analysis for Multiple Groups

Introduces methods to identify which groups differ after a significant homogeneity result. Extends the test from an omnibus finding to actionable group comparisons.

Lesson 2 • Designing a Homogeneity Study

Covers how to plan data collection for comparing categorical distributions across independent groups. Addresses sampling strategy and group definition.

Lesson 3 • Executing the Homogeneity Test

Applies the chi-square procedure to multi-group frequency data with full step-by-step guidance. Reinforces the shared computation with the independence test.

Lesson 4 • Applied Homogeneity Case Studies

Practises the homogeneity test on realistic multi-group datasets from business, health, and social research. Builds decision-making fluency across contexts.

Lesson 1 • Effect Size Measures for Chi-Square

Covers Cohen's w, Cramér's V, and phi as standardised effect size indices. Connects each measure to the specific test type and table dimension.

Lesson 2 • A Priori Power Analysis

Teaches how to calculate required sample size before data collection using effect size and desired power. Directly applicable to study design and grant proposals.

Lesson 3 • Practical Sample Size Planning

Integrates effect size, power, and design constraints into realistic sample size decisions. Learners practise planning for goodness-of-fit, independence, and homogeneity tests.

Lesson 4 • Statistical Power Fundamentals

Defines power as the probability of detecting a true effect and explains its determinants. Builds the conceptual basis for sample size planning.

Lesson 1 • Fisher's Exact Test

Introduces Fisher's exact test as the preferred method for small 2×2 tables. Covers the hypergeometric basis and exact p-value computation.

Lesson 2 • Likelihood Ratio Chi-Square (G-Test)

Presents the G-test as a likelihood-based alternative with better properties for sparse data. Compares G-test and Pearson chi-square in practical scenarios.

Lesson 3 • McNemar's Test for Paired Data

Covers McNemar's test for comparing proportions in matched or repeated-measures designs. Addresses the independence assumption violation in paired categorical data.

Lesson 4 • Limitations of the Standard Chi-Square Test

Examines conditions where chi-square produces unreliable results, including sparse tables and small samples. Motivates the need for alternative procedures.

Lesson 1 • Integrating Chi-Square into Mixed-Method Studies

Shows how chi-square findings complement qualitative and quantitative methods in mixed designs. Builds capacity to position chi-square within broader research frameworks.

Lesson 2 • Writing Up Chi-Square Research

Covers professional standards for reporting chi-square analyses in academic and applied reports. Addresses tables, figures, and narrative interpretation.

Lesson 3 • Controlling for Confounding Variables

Introduces stratified analysis and the Mantel-Haenszel method to control for third variables. Extends chi-square from bivariate to multivariate categorical analysis.

Lesson 4 • Selecting the Right Chi-Square Test

Provides a decision framework for matching research questions and data structures to the correct chi-square procedure. Synthesises all tests covered in prior chapters.

Lesson 1 • Evaluating and Critiquing Chi-Square Studies

Develops critical appraisal skills for evaluating published chi-square analyses. Learners can identify methodological flaws and assess the validity of reported conclusions.

Lesson 2 • Automating Chi-Square Workflows

Introduces scripting and automation to run chi-square analyses at scale across multiple datasets. Builds efficiency for analysts handling large or recurring categorical data tasks.

Lesson 3 • Chi-Square in Quality and Process Improvement

Applies chi-square to defect analysis, process monitoring, and quality audits. Demonstrates how categorical data testing drives continuous improvement decisions.

Lesson 4 • Chi-Square in Survey and Market Research

Uses chi-square to analyse segmentation, preference, and attitude data from surveys. Connects statistical findings to strategic business and policy decisions.