The standard general concept to find the ANOVA table was method of moments (MM); this approach relied strongly on normality assumptions and it is sub-optimal in comparison with standard least-squares (LS) procedures. In addition if the data are unbalanced a lot of ANOVA's theoretical concepts are seriously perplexed and this makes the estimation even more questionable. The user @Placidia has given two excellent answers on the matter herehere and herehere. MM is sometimes still used in one-way and two-way ANOVA because of its ease to code it up conceptually but essentially all $n$-way ANOVA routines now rely on LS. I have seen some (usually clustering) algorithms using MM because they are easier to code up and faster to converge; they serve as good hot-start points for optimization tasks.
(This post is an over-sized comment.)
