The test statistic for the analysis of variance (ANOVA) is called the $F$ statistic. It represents a ratio of two distinct estimates of the population variance based on the sample data. Specifically, it is calculated by dividing the mean squares between groups ($MS_B$) by the mean squares within groups ($MS_W$). The mathematical formula is expressed as $F = \frac{MS_B}{MS_W}$. By computing this ratio, researchers can mathematically determine whether the differences observed among the sample means are larger than would be expected by random chance.