Because ANOVA is right-tailed, a high F statistic corresponds to a p-value that is:

1. The p-value is the tail area beyond the observed statistic. 2. A one-way ANOVA test is always right-tailed. 3. A high F statistic therefore leaves only a small area in that tail. 4. So a high F statistic corresponds to a low p-value. 5. It is then likely that we will reject the null hypothesis. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 13 'The F Distribution and One-Way ANOVA', sections 13.1-13.4_