Goodness-of-fit test

As explained in Effective Data Analysis

A goodness-of-fit test is a chi-square test that compares observed category frequencies in one sample with expected frequencies.

A goodness-of-fit test is a chi-square test that compares observed category frequencies in one sample with expected frequencies. It asks whether the observed distribution differs from an expected distribution. section 5.2.3

Use it to identify disproportionality against fixed expectations or relative proportions. Distinguish it from tests of independence, which compare two categorical variables, and tests for trend, which examine patterns across time or groups. section 5.2.3

Interpret the comparison by considering:

• Observed frequencies: the category counts or proportions collected from the sample. section 5.2.3
• Expected frequencies: the counts or proportions predicted under the null hypothesis of no differences between categories. section 5.2.3
• Sample size: larger samples detect smaller differences more readily, while smaller samples make differences harder to detect. section 5.2.3

Figure 5.12 Breakdown of the equation for the X² (chi-square) test

Use the chi-square equation breakdown to connect each category’s observed and expected frequency difference to the overall test statistic. section 5.2.3

How Effective Data Analysis covers it

How deep it goes

Explains the observed-versus-expected comparison, test variants, and sample-size sensitivity.

Examples

Uses category counts or dataset proportions as the observed and expected inputs.

What it assumes

Assumes categorical frequencies and a null expectation of no differences between categories.

What you can do after

Evaluate whether one sample’s categorical distribution differs from its expected distribution.

How it connects

Connects expected frequencies and null hypotheses with chi-square tests of independence and tests for trend.

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Related concepts

• chi-square testkind of · A chi-square test is a statistical hypothesis test that uses a chi-square-distributed statistic to evaluate hypotheses about categorical data, goodness of fit, or variance.
• goodness-of-fit measuremeasures · A goodness-of-fit measure quantifies how closely a statistical model or representation agrees with observed data or specified relationships.

This explainer was generated by Manning's knowledge graph from the text of Effective Data Analysis. The section links point to the parts of the book it draws on.