I probably view it too pragmatic but to me, the F statistic is merely a result of a calculation that is used to (magically) determine the value that I'm really interested in: the p. APA, though, wants the F reported along with the degrees of freedom (and the p). Why is knowing the F and the df relevant? Is this used as a short test whether my calculation was right? Or is there any information in the F value that I don't get?
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1$\begingroup$ Drives me crazy. People write F=17.435, p<0.05. (And they don't report the df, of course.) $\endgroup$– Jeremy MilesCommented Sep 1, 2015 at 19:54
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I can't speak for the APA but I see value as a reader in having information on degrees of freedom and F statistics. Degrees of freedom provide reassurance about the scale of the study. The F statistic, as the ratio of explained variance to error variance, contains important information about how effective the model was.
This cuts both ways. With a significant $p$ value based on a high F but few degrees of freedom, I might worry about issues specific to a particular data set and a spurious or non-generalizable result. With low F but many degrees of freedom, I might wonder if a statistically significant result really is substantial enough to consider significant for practical application.
So please report these as a courtesy to your readers even if a journal doesn't require them.
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1$\begingroup$ +1. Also, I suspect people doing meta-analyses appreciate explicit reports of effect sizes (and the F statistic can be interpreted as that). One might go so far as to argue--and a great many psychologists are now doing so--that one should not be focused on the p-value to the exclusion of all else. $\endgroup$– whuber ♦Commented Sep 2, 2015 at 19:47