# Compare p values of ANOVA and $\chi^2$ test

I have dataset with different types of features (numeric/continuous and binary). Altogether 66 features.

I want to find a small subset of features that is sufficient for a multi class classification problems (3 classes).

Therefore, I would like to do a filter-based feature selection using a technique that gives a p-value per feature so that I can take the best 5 features based on their p-values, for example.

For the numeric features I can use the ANOVA test to get the p-values and for the binary features I could use $$\chi^2$$ test to get the p-values.

Now I have the following two questions:

1. Can I compare the p-values computed by ANOVA and the p-values computed by $$\chi^2$$ to rank all features based on the p-values?
2. Is it okay to use ANOVA on the binary features (the binary features are treated as if they were continuous) and compare the p-values to the p-values of numeric/continuous features?