THE INTRODUCTORY OFFER PERIOD
 

 

 

 

 

 

 

 

 

 

 

 

 

 

For example, suppose the target variable is a binary flag indicating whether or not customers continued their subscriptions at the end of the introductory offer period and the proposed split is on acquisition channel, a categorical variable with three classes: direct mail, outbound call, and email. If the acqui­ sition channel had no effect on renewal rate, we would expect the number of renewals in each class to be proportional to the number of customers acquired through that channel. For each channel, the chi-square test subtracts that expected number of renewals from the actual observed renewals, squares the difference, and divides the difference by the expected number. The values for each class are added together to arrive at the score. the chi-square distribution provide a way to translate this chi-square score into a probability. To measure the purity of a split in a decision tree, the score is sufficient. A high score means that the proposed split successfully splits the population into subpopulations with significantly different distributions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The chi-square test gives its name to CHAID, a well-known decision tree algorithm first published by John A. Hartigan in 1975. The full acronym stands for Chi-square Automatic Interaction Detector. As the phrase “automatic inter­ action detector” implies, the original motivation for CHAID was for detecting Team-Fly® Decision Trees 183 statistical relationships between variables. It does this by building a decision tree, so the method has come to be used as a classification tool as well. CHAID makes use of the Chi-square test in several ways—first to merge classes that do not have significantly different effects on the target variable; then to choose a best split; and finally to decide whether it is worth performing any additional splits on a node. In the research community, the current fashion is away from methods that continue splitting only as long as it seems likely to be useful and towards methods that involve pruning. Some researchers, however, still prefer the original CHAID approach, which does not rely on pruning. The chi-square test applies to categorical variables so in the classic CHAID algorithm, input variables must be categorical. Continuous variables must be binned or replaced with ordinal classes such as high, medium, low. Some cur­ rent decision tree tools such as SAS Enterprise Miner, use the chi-square test for creating splits using categorical variables, but use another statistical test, the F test, for creating splits on continuous variables. Also, some implementa­ tions of CHAID continue to build the tree even when the splits are not statisti­ cally significant, and then apply pruning algorithms to prune the tree back.