One-way Analysis of Variance (ANOVA) is a parametric statistical hypothesis test used to determine whether there are statistically significant differences between the means of three or more independent groups within the domain of inferential statistics. The core mechanism relies on partitioning total variance into between-group and within-group components, calculating an F-statistic as their ratio to assess if observed deviations exceed chance expectations under a normal distribution assumption with homogeneity of variances. This method serves as the direct extension of the t-test for scenarios involving multiple groups, allowing researchers to reject or fail to reject a null hypothesis stating all population means are equal without conducting pairwise comparisons during the initial test phase.
Prerequisite chain context: requires Homogeneity of Variance Principle for ANOVA Tests.