Compositional data looks like this: $[p_1, ...., p_n]$ where $\sum p_i = 1$.
My question is, I know that we can analyze this using log-ratio analysis but ...
Why not just use anova? Take each of the $n$ components, and use them as factors. So each data row is turned into $n$ rows, with response $p_1, ...., p_n$, and the actual component is then a factor.
For example, if we have % of wage spent on milk, bread, and butter, then instead of treating [20%, 10%, 70 %] as a response, we can treat 20% as a "percent money spent on item", where "item" is the factor, here milk.
Then if the mean for milk is higher or lower, it tells us how much we spend on it compared to other items.