Adequate sample sizes for omnibus ANOVA tests do not necessarily provide sufficient statistical power for post hoc multiple comparisons typically performed following a significant omnibus F test. Results reported support a comparison-of-most-interest approach for sample size determination in ANOVA based on effect sizes for multiple comparisons.
Brooks, Gordon P. and Johanson, George A.
"Sample Size Considerations for Multiple Comparison Procedures in ANOVA,"
Journal of Modern Applied Statistical Methods:
1, Article 10.
Available at: http://digitalcommons.wayne.edu/jmasm/vol10/iss1/10