Chi-square (x2) is a statistical measure that conducts a significance test on the relationship between the values of a feature and the class. The x2 statistic determines the similarity of adjacent intervals based on some significance level.
It tests the hypothesis that two adjacent intervals of a feature are independent of the class. If they are independent, they should be merged; otherwise they should remain separate.
The top-down method based on chi-square is Chi Split. It searches for the best split of an interval, by maximizing the chi-square criterion applied to the two sub-intervals adjacent to the splitting point: the interval is split if both sub-intervals substantially differ statistically. The Chi Split stopping rule is based on a user-defined chi-square threshold to reject the split if the two sub-intervals are too similar. The bottom-up method based on chi-square is Chi Merge. It searches for the best merge of adjacent intervals by minimizing the chi-square criterion applied locally to two adjacent intervals: they are merged if they are statistically similar. The stopping rule is based on a user-defined Chi-square threshold to reject the merge if the two adjacent intervals are insufficiently similar.