When creating a classification model, should predictors with little correlation to the response variable be included in the model? I am building a predictive model designed to predict attrition within my organization.  I am trying to decide whether to add certain predictors to my model.  I used a Kruskal-Wallis rank sum test to check the correlation between a few of my predictor  variables and my response variable and found that the predictors are independent from my response.  Should I still include these variables in my model? I am leaning towards no due to the lack of correlation with my response variable but don't want to discard a potential "split" in my decision tree.  My data set contains 8,225 observations and 173 columns which I have been using as predictors.
In general, a Kruskal-Wallis test (or any other univariate test) cannot guarantee that there are no useful interactions with other features that a decision tree might still pick up. That means you won't know for sure until you try it.

You can test the performance with and without these "weak" features and compare results. Make sure you control for overfitting when including all features. Alternatively, after fitting the decision tree, you can look at the target response when varying the feature values ("partial dependence").