Chi-square test
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.
Statistics Slam Dunk
A chi-square test is a statistical test based on a chi-square-distributed statistic for assessing categorical-data relationships or distributional differences.
- How it is used
- Tests whether categorical variables such as prior rest and game outcomes are related.
- How deep it goes
- Defines independence hypotheses and p-value decisions, then demonstrates running chisq.test() on a contingency table.
- Examples
- Uses NBA days off versus wins and losses, survey sentiment versus marital status, political beliefs, and restaurant customer counts.
- What you can do after
- Apply it via base R’s chisq.test() to assess categorical relationships from a contingency table.
Effective Data Analysis
A chi-square test is a statistical test that evaluates categorical data by comparing observed frequencies with frequencies expected under a specified hypothesis.
- How it is used
- Uses categorical comparisons when both independent and dependent variables are categorical.
- How deep it goes
- Explains test variants, observed-versus-expected frequencies, contingency tables, calculations, and pairwise follow-up comparisons.
- Examples
- Demonstrates recommender versions, countries, user clicks, expected-frequency tables, Python output, and an observed-versus-expected heatmap.
- What you can do after
- Apply it via SciPy to compare categorical frequencies and inspect expected counts, p-values, and cell-level differences.
Statistics Every Programmer Needs
A chi-square test is a statistical hypothesis test that compares observed categorical counts with expected counts to assess whether their discrepancy is statistically significant.
- How it is used
- Tests whether observed leading-digit counts conform to Benford’s law for anomaly detection and statistical validation.
- How deep it goes
- Derives expected counts, the chi-square statistic, degrees of freedom, and p-value interpretation, while requiring sufficient records.
- Examples
- Uses leading digits in world population counts, with tabulated observed counts, expected counts, and category contributions.
- What you can do after
- Diagnose whether categorical counts significantly depart from an expected distribution using Python’s SciPy implementation.
Read how Statistics Every Programmer Needs explains chi-square test →
Related concepts
- hypothesis testingkind of · Hypothesis testing is a formal statistical procedure that uses observed data to evaluate evidence about a specified hypothesis, often a null hypothesis.
- non-parametric testkind of · A non-parametric test is a statistical test that evaluates evidence without requiring a specified parametric distributional form for the data.
- categorical datauses · Categorical data consists of values representing membership in a discrete set of named or ordered categories rather than measured numerical magnitudes.
- contingency tableuses · A contingency table is a tabular summary of counts or other measures for combinations of categories from two or more categorical variables.
- t-testcontrasts with · A t-test is a statistical hypothesis test that uses a t-distributed statistic to assess a mean or difference in means under specified assumptions.
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