Chi-Squared and ANOVA

The t-tests from the previous lesson compare one or two group means. But what if you need to compare three or more groups, or analyse categorical data? This lesson introduces two powerful families of tests: chi-squared tests for categorical data and ANOVA for comparing multiple group means.

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Chi-Squared Tests

The chi-squared (χ²) test is used when data consists of counts or frequencies in categories.

1. Chi-Squared Goodness-of-Fit Test

Tests whether the observed frequencies of a categorical variable match an expected distribution.

Hypotheses:

H₀: The observed frequencies match the expected distribution
H₁: The observed frequencies do not match the expected distribution

Test Statistic:

χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ

Where:

• Oᵢ = observed frequency for category i
• Eᵢ = expected frequency for category i

Degrees of freedom: df = k − 1, where k is the number of categories

Example: A die is rolled 60 times. If fair, each face should appear 10 times.