analogy for pearson r statistics for binary classification task
The Pearson Chi-Squared test may give you what you need:
https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test 

This is a good resource for analyzing categorical data:  https://en.wikipedia.org/wiki/List_of_analyses_of_categorical_data

Also, confusion matrices can be very helpful:  https://en.wikipedia.org/wiki/Confusion_matrix