Usually, the one-way ANOVA is of no scientific interest at all. What the researcher really wants is the pair-wise comparison of the group means, what is done by post-hoc tests. Such post-hoc tests are logically completely independent from an ANOVA, tand they do control the family-wise error-rate absolutely independently of an ANOVA (there are very few special exceptions of ancient methods).

So the fundamental mistake is that the authors think they would need an ANOVA at all, but all they really need is, for instance, to report the results of the post-hoc tests (like Dunnett or Tukey).

The value of an ANOVA emerges in more complex models where nested models should be compared that dffer in groups of parameters. A nitpicker may insist that a one-way ANOVA does just this comparing a model with all the parameters associated with a cetagorical predictor with an "intercept-only model", and that it tells us something about the usefulness of this predictor as a whole. That's correct, but this is not adding any information that is relevant for the researcher. And it is not helpful, since the post-hoc tests do control the family-wise error rates. It can be rather confusing that the ANOVA F can be "significant" but yet none of the pair-wise comparisons reveals a "significant" t-value (and vice versa!). Hence, doing one-way ANOVAs is usually off-the mark and pointless in itself, and therefore it is pointless to report statistics obtained from the ANOVA.

The mean part in this story is that many stats software provide post-hoc tests as a kind of appendix to ANOVAs - so you must select "ANOVA" from some menu first to be able to do post-hoc tests at all. This may have made many people think that the ANOVAs are required (logically) to do post-hoc tests. But this is wrong. During the ANOVA some interim results are calculated that are also used in post-hoc tests, and programmers are lazy (or efficient, to use a more positive word)...

Much more interesting questions that is generally widely dodged are:

- do I need to control a family-wise error-rate?

- what rate is acceptable?

- what is the actual family of tests?

After all my conclusion is that the whole ANOVA-post-hoc-thing is done (almost) only because reviewers want to see it. It has (almost) no substantive scientific justification, and most authors more or less blindly follow "instructions" they don't really understand, hoping that the paper gets published*. That's that dark side of science.

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* that's ok, I mean this is a fault of the system and not of the people. And luckily there are many brilliant scientists who do good substantive research despite the silly habits that have settled in the scientific community.

Thanks Jochen for your elaborate comment. I believe that conducting ANOVA was important in the older days when one would hand compute post-hocs only if ANOVA showed a significant value. If ANOVA shows no significance then one would just not get into taking pains to compare each treatment with other. In today's world of computer based statistical calculations reporting ANOVA when post-hoc values have been reported makes no sense to me. Reviewers demand it but probably editors should step in (provided they understand the meaning of science behind statistical analysis).