I have 14,000 data sets, and I'm going to do Anova in 5 groups. The problem is that the size of Group A is 10,000, but the size of Group B is only 300. In general, I understand that the unequal of sample size in Anonva is not a very serious problem. However, my concern is that even if the sample sizes between the groups are extremely different, there is still no problem performing Anova. Please let me know if there is a specific value (e.g. effect size) that I need to consider or report in this analysis. Thank you.
Provided that the assumptions for ANOVA hold, there is no inherent problem with differing group sizes. The error estimates for the smaller groups (and error estimates for their differences from other groups) will necessarily be larger than those for the larger groups. It's usually wise to provide means and standard deviations for each group in addition to the overall ANOVA results.
If you do all 10 pairwise comparisons among the 5 groups make sure to correct for multiple comparisons. That's one place where the unequal group sizes might pose a problem, as range tests like Tukey's assume equal group sizes. See the Wikipedia entry on the Tukey test for Kramer's adaptation to handle unequal groups sizes. Alternatively, use a Holm-Bonferroni or similar correction directly on p-values.