One-way ANOVA for multiple features? I have 60 continuous features (i.e., lab results) for 35,000 patients, and the patients are divided into three groups. I want to evaluate each feature to find out what the differences are between the groups.
Here is my plan:

*

*For each feature, iteratively run a one-way ANOVA independently.

*After 60 ANOVA are run, correct for multiple comparisons using Bonferroni correction.

*Using only the significant features (as per the ANOVA with Bonferroni), run a post-hoc analysis (Tukey's HSD) for each one.

*Use the p-value results from Tukey's HSD to confirm any significant pairwise differences between the groups. Assume there is no need for additional Bonferroni correction at this stage.

Is this an acceptable approach? Or do I need to use a multi-way ANOVA for this? Or MANOVA?

Discriminant analysis as suggested in a previous answer is a possibility: you should realize, however, that only indirectly (through the coefficients of the linear discriminant functions) will tell you which features appear to be different among groups.
A Bonferroni correction in the case of 60 simultaneous tests will declare a feature as significant only if the individual ANOVA for that feature rejects the null hypothesis at the $\alpha/60$ significance level, were $\alpha$ is the desired nominal level. You would pick as significant only results for which the evidence is really overwhelming.
MANOVA (much like discriminant analysis) has the advantage over multiple univariate ANOVAs that it accounts for possible correlation among features. On the other hand (much like linear discriminant analysis) it assumes equal covariance matrices across groups, which is a quite strong assumption.
