If a statistic doesn't reveal a significance, do I have to calculate power for it? Following the design and data described in this question, I did a simple one-way within-subjects repeated-measures (RM) ANOVA and found some significant p-values. I then applied non-orthogonal post-hoc Tukey's HSD tests, and when I got significant results I applied Holm-Bonferroni (1979) correction. Whenever some p-values survived the FWER correction, I calculated 95% CIs and mean for the associated pairwise comparisons.
My question is: If I don't observe a significant result at any of the above steps, do I have to carry out a power analysis for the RM ANOVA, apply Tukey's HSD test or Holm-Bonferroni adjustments, or do I simply report results from the RM ANOVA without doing the power analysis?
The problem is that I'm starting to immerse in biostatistics only after my experiments, and unfortunately I didn't run a power analysis beforehand.  
 A: As an aside, Tukey's doesn't depend on the ANOVA results being significant; you can have significant pairwise differences even when the overall ANOVA is not significant.
That is to say, if you're going to be doing Tukey-corrected pairwise comparisons, don't bother checking for overall significance first.  If you only run the Tukey comparisons after getting a significant overall p-value, you are over-correcting.
(I'm confident that this is true with regular ANOVA; it's possible that with repeated measures or non-orthogonality something else happens; anyone care to chime in?)
Finally, to agree with Freya but to provide a little more guidance, instead of a post-hoc power test, a more reasonable thing to report would be the confidence intervals; they show exactly how big a difference your experiment could have detected, which is usually what people are after when they want a post-hoc power test anyway.
A: Another good discussion of the pitfalls of post-hoc power estimation is found in:
Gerard, P. D., D. R. Smith, and G. Weerakkody.  1998.  Limits of retrospective power analysis.  Journal of Wildlife Management 62:801-807 [link].
A: Most text books argue that it is only proper to do a post hoc such as Tukey's only with a significant f.   If you chose planned comparison based on theory, a non significant F would be okay ...  Tukey's is a fairly conservative test that typically won't show significance if f is not significant.  What value are you using for mean square within to calculate Tukey's? The confidence intervals are also supposed to use mean square with rather than separate variance estimates.  
A: The hardline view on post-hoc power calculation is: don't do it as it's pointless.  Russ Lenth from the University of Iowa has an article on this topic here  (He also has an amusingly facetious Java applet for post-hoc power on his website).
