# How to determine if my sample size was large enough to detect an effect post-hoc?

I did an experiment and afterward conducted an ANOVA where I got results that were not significant:

            Df Sum Sq Mean Sq F value Pr(>F)
type         1   1.91   1.910   0.735 0.3951
sex          1   7.48   7.482   2.878 0.0955 .
type:sex     1   0.05   0.048   0.018 0.8927
Residuals   54 140.37   2.599


I'm mostly interested in the type*sex interaction here.

My sample size is 16, pretty similar to other studies in this field (sample size usually 20 more or less). I've read that it's pointless to do a power analysis after the fact so now I'm wondering what sort of analysis I can do to test if my sample size was large enough to detect an effect.

When looking at the graphs they are in the expected direction for this variable and also for two other (out of 3) variables however they all similarly have very high p-values.

• In addition to the answer from @rvl, a well respected expert on this issue, note that the main effects in your model dwarf the interaction term of interest to you. Even if an extremely large study showed that this interaction was "statistically significant," would it really be practically significant? – EdM Mar 23 '18 at 1:23