> We split the adults aged 50 or older into groups reflecting their average level of drinking, from non-drinkers through to those drinking three or more drinks a day.
The decision to split a naturally continuous or interval variable into discrete groups and then compare those groups has no valid statistical purpose. It serves no advantage over the regression alternative but it does lower the power of the analysis. ANOVA really just needs to die already. It became popular in the social sciences because it was a feasible way of doing inferential statistics back when computations were done with a pen and paper. Now we have computers and there's no excuse not to use better methods, an obvious alternative being linear regression.
Boycott bad stats. If you are a reviewer then hold the field to a higher standard.