The log-rank test is a non-parametric statistical hypothesis test used in survival analysis to compare the distribution of time-to-event between two or more independent samples under the null hypothesis that their survival functions are identical. It operates by analyzing the discrepancy between observed and expected event occurrences across multiple groups at distinct failure times, utilizing the Kaplan-Meier estimator framework where censored observations contribute to risk sets but do not count as events. The test statistic asymptotically follows a chi-square distribution with degrees of freedom equal to the number of groups minus one, allowing for significance determination based on whether group-specific survival distributions differ significantly from each other in time-to-event domains such as medical epidemiology and reliability engineering.
Prerequisite chain context: requires Kaplan-Meier Curve Survival Analysis in Statistics.