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

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    $\begingroup$ Please edit your post with a full citation for the article, not just the link, as links can die. Thanks! $\endgroup$ – Dave May 17 at 21:42

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