As far as I know, ANOVA results can be interpreted with respect to mean differences between 2 or more groups. But, we can not make any inference on which mean is larger or smaller in a statistically significant way based on an ANOVA.
However, I have recently read a study (article) where a significant p-value together with absolute mean differences was interpreted with respect to directionality ("While the more educated respondents experienced significantly more lifetime discrimination (F = 2.68, p <.05)").
This, without an additional one-sided t-test or such being performed. Is this a correct way of statistically interpreting an ANOVA?
Article: Yoon et al. (2019): Perceived discrimination and mental health among older African Americans: the role of psychological well-being