To determine if there are significant differences among group means in an ANOVA, researchers evaluate the computed $F$ statistic by finding its corresponding $p$-value or comparing it against a predetermined critical value from an $F$ table. If the computed $F$ ratio is greater than the critical value, the associated $p$-value is less than the alpha level (typically $.05$). In this outcome, the researcher rejects the null hypothesis and concludes that the population means differ. Conversely, if the $F$ ratio is less than the critical value, resulting in a $p$-value greater than $.05$, the researcher retains the null hypothesis, concluding there is insufficient statistical evidence to claim any differences exist.