Statistics

Chi-square

This statistic is distributed according to a chi-square distribution with degrees of freedom equal to the difference between the number of parameters under the alternative hypothesis and the number of parameters under the null hypothesis.

Cramer’s V

Notation:

N = Total number of observations

min(i-1)(j-1) = Minimum of row dimension minus 1 and column dimension minus 1

F-test

Gini

Notation:

N = Total number of observations

Information Value (IV)

The IV of a predictor is related to the sum of the (absolute) values for WoE over all groups. Thus, it expresses the amount of diagnostic information of a predictor variable for separating the Goods from the Bads.

Kolmogorov-Smirnov (KS) test

For all Good observations, predicted probability of Bad is computed, that is the relative frequency of bad cases in the bin a Good observation is placed. This process is repeated for all Bad observations. The KS test is then completed with the Good/Bad indicator as the group variable and the predicted probability of Bad as the response.

Significance level (p) approximation is based on the formula:

Logit Transformation (Logg Odds)

Mean

Somer’s D

If ties are present:

If ties are not present:

Note: Sorting of cases for calculation of Somer’s d is based on the relative frequency of bad, that is, estimated probably of bad.

Notation:

t = total number of pairs with different responses of good/bad

nc = number of pairs of cases where the case with the lower ordered response value has a lower predicted mean score than the case with the higher ordered response value.

nd = number of pairs of cases where the case with the lower ordered response value has a higher predicted mean score than the case with the higher ordered response value.

Weight of Evidence (WoE)

The value of WoE is 0 if the odds of Relative Frequency of Goods / Relative Frequency Bads is equal to 1. If the Relative Frequency of Bads in a group is greater than the Relative Frequency of Goods, the odds ratio is less than 1 and the WoE is a negative number; if the Relative Frequency of Goods is greater than the Relative Frequency of Bads in a group, the WoE value is a positive number.