Chi-Square Tests and Categorical Data Analysis

Categorical Data Analysis: Chi-Square Tests

Shifting Your Thinking for Categorical Data

When analyzing categorical data, a significant shift in thinking is required compared to parametric tests. Instead of measuring characteristics inside people (e.g., height, weight), we are counting across them. This type of analysis typically involves nominal or ordinal level data for the dependent variable. We transition from parametric tests, which assume underlying distributions, to nonparametric tests, which do not.

Introduction to Chi-Square ($\chi^2$) Tests

Chi-square ($\chi^2$) is a foundational class of nonparametric tests. I will introduce two primary chi-square tests and their associated effect sizes:

• Chi-square Goodness-of-Fit Test: Used when you have one independent variable.

• Chi-square Test of Independence: Used when you have two independent variables (though this lecture focuses primarily on goodness-of-fit).

Two effect sizes commonly associated with chi-square tests are:

• Phi ($\phi$)

• Cramer's V ($V$)

The Nature of Nonparametric Data

When dealing with categorical data, you are fundamentally working with frequency data – simple counts of observations within categories. This type of data has limitations:

• Inability to Calculate Means and Standard Deviations: These fundamental descriptive statistics, often referred to as