## 3 Methodology
### QUEST Algorithm for Data Mining
For each continuous or ordinal independent variable X, compute the smallest \(p\)-value using the ANOVA F-test to test if all categories of the dependent variable have the same mean as X and compute the smallest \(p\)-value using [PERSON]'s chi-squared (\(\chi^{2}\)) statistic. 7. For X in continuous_ordinal_vars:
8. \(p\_value\_f\_test=\) compute_\(p\_value\_using\_anova\_f\_test(X)\)
9. \(p\_value\_chi\_squared=\) compute_\(p\_value\_using\_chi\_squared(X)\)
10. For each categorical independent variable, perform [PERSON]'s \(\chi^{2}\) test for independence between Y and X, and find the \(p\)-value using the \(\chi^{2}\) statistic. 11. For X in categorical_vars:
12. \(p\_value\_chi\_squared=\) compute_\(p\_value\_using\_chi\_squared(X)\)
13. Identify the independent variable with the smallest \(p\)-value and denote it as X*. 14. smallest_\(p\_value=\) min(\(p\_value\_f\_test,p\_value\_chi\_squared)
15. X* = independent_var_with_smallest_\(p\_value\)
16. If the smallest \(p\)-value is less than \(\alpha\)/M, where M is the total number of independent variables, then SELECT X* as the predictor for splitting the node. Otherwise, go to step 4. 17. If smallest_\(p\_value<\) alpha/M:
18. selected_predictor = X*
19. Else:
20. continue_to_step_4 = True
21. Calculate [PERSON]'s F statistic based on the absolute deviation of X from its class mean to test if the variances of X for different classes of Y are the same for each continuous independent variable X and find the \(p\)-value for the test. 22. For X in continuous_vars:
23. Levene_\(f\_statistic<\) calculate_levene_f_statistic(X)
24. \(p\_value\_levene\_test=\) find_\(p\_value\_for\_levene\_test(levene\_f\_statistic)
25. Identify the independent variable with the smallest \(p\)-value and denote it as
26. X**. 27. smallest_\(p\_value=\) min(\(p\_value\_levene\_test\))
28. X** = independent_var_with_smallest_\(p\_value\)
29. If the smallest \(p\)-value is less than \(\alpha\)/(M + M1), where M1 is the number of continuous independent variables, then SELECT X** as the split independent variable for the node. Otherwise, do not split this node. 30. If smallest_\(p\_value<\) alpha/(M + M1):
31. selected_split_var = X**
32. Else:
33. do_not_split_node = True
```  
**Algorithm 1**Pseudocode for the QUEST algorithm  
Step 6: Calculate [PERSON]'s F statistic based on the absolute deviation of X from its class mean to test if the variances of X for different classes of Y are the same for each continuous independent variable X and find the \(p\)-value for the test. Identify the independent variable with the smallest \(p\)-value and denote it as X**. If the smallest \(p\)-valueis less than \(\alpha/(\text{M}+\text{M}1)\), where M1 is the number of continuous independent variables, then SELECT X** as the split independent variable for the node. Otherwise, do not split this node. Step 7: Repeat steps 3 to 6 until all nodes are either leaf nodes or cannot be split further based on the significance level \(\alpha\). Further, the established equations for Pearson's chi-squared statistic and ANOVA F statistic are presented. The equation for Pearson's chi-squared statistic:  
\[\chi 2=\sum_{i,\ j}\frac{\left(O_{ij}-E_{ij}\right)^{2}}{E_{i\overline{j}}} \tag{1}\]  
where \(O_{ij}\) is the observed value, \(E_{ij}\) is the expected value for the _ith_ row and _jth_ column of the data cell. The equation for the ANOVA F statistic:  
\[\text{F}=\frac{\sum n\eta\left(\overline{X}j-\overline{X}\right)^{2}/(k-1)}{ \sum\sum\left(X-\overline{X}j\right)^{2}/(N-k)} \tag{2}\]  
where \(\eta\) is the sample size in the _jth_ group, \(\overline{X}j\) is the sample mean, and the \(\overline{X}\) is the overall mean. \(N\) is the total number of observations, and \(k\) is the number of independent groups. In Table 2. the methodology summary is presented.