Pearson's Chi-Squared Test

Pearson's chi-squared test is a method for testing whether an observed pattern of categorical data differs significantly from what would be expected under a stated hypothesis, comparing a summary statistic built from the squared differences between observed and expected counts against the chi-squared distribution. Karl Pearson introduced it in his 1900 paper On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is such that it can be Reasonably Supposed to have Arisen from Random Sampling, published in the Philosophical Magazine. It became one of the most widely used tools in statistics for testing goodness of fit and independence in tables of counted data, and its introduction is often credited with beginning the mathematical theory of statistical hypothesis testing.