I am doing a one-way ANOVA of a response variable (Y) on a treatment factor (T) of 7 levels. However, for each treatment, I have only 2 observations (or replicates). The ANOVA result shows the the means across the treatment are highly significant (p<0.001). I have check the normal and constant-variance assumptions and seems that my data does not violate these assumptions.
My question is: Can I trust the result of ANOVA, even if the sample size is extremely small (n=2*7=14)?
The first question that comes to my mind is the power of my test. Since my ANOVA has obtained an effect size of 0.9. I conducted a power analysis (using Q*Power.3) to see how many samples are needed to obtain such effect size with significance level of 0.05 and power of 0.8. The result showed that I need at least 28 samples. Since I have much fewer samples than required, does it mean that my ANOVA results are not reliable?