ANOVA is not the same of Duncan test. ANOVA means variance fragmentation (analysis in the sense of Kant) and it is an exact test for the probability of the difference of the averaged square sum of variation between treatments (MSA) with the averaged square sum of variation within treatments (S2). If Ho: MSA/S2>1 have probability p
your question needs to be more specified, in statistics there is no such a one model fit the case, but you sometimes have more than one option but you need to choose the best depends on your data, purpose, questions, and so on. So there are many advantages for ANOVA it helps you to determine the significant different between groups which is more than tow ( in case of one way ANOVA ) and POST HOC tests such as Dunken, LSD, Sheffey ,...... Can help you to rank groups means. Totally agree with Miguel and I also personally prefer Tukey it is moderate in judgment .
ANOVA is being used to test the significant mean difference in two. further group should have three or more sub group. Like Education (Illiterate, primary, High School ....) to Test with Age (0-10, 10-20, 20-30 ........) one you find the significant then you may proceed for Post Hoc Multiple comparison which will show that if there is mean difference in group then within the group in which sub group differences occur .