In the following example, the response variable has only two classes: whether to play tennis or not. But the following table has been compiled based on various conditions recorded on various days. Now, our task is to find out which output the variables are resulting in most significantly: YES or NO.

1. This example comes under the Classification tree:

2. Taking the Humidity variable as an example to classify the Play Tennis field:
   • CHAID: Humidity has two categories and our expected values should be evenly distributed in order to calculate how distinguishing the variable is:

Calculating x² (Chi-square) value:

Calculating degrees of freedom = (r-1) * (c-1)

Where r = number of row components/number of variable categories, C = number of response variables.

Here, there are two row categories (High and Normal) and two column categories (No and Yes).

Hence = (2-1) * (2-1) = 1

p-value for Chi-square 2.8 with 1 d.f = 0.0942

p-value can be obtained with the following Excel formulae: = CHIDIST (2.8, 1) = 0.0942

In a similar way, we will calculate the p-value for all variables and select the best variable with a low p-value.

• ENTROPY:

Entropy = - Σ p * log ₂ p

In a similar way, we will calculate information gain for all variables and select the best variable with the highest information gain.

• GINI:

Gini = 1- Σp²

In a similar way, we will calculate Expected Gini for all variables and select the best with the lowest expected value.

For the purpose of a better understanding, we will also do similar calculations for the Wind variable:

• CHAID: Wind has two categories and our expected values should be evenly distributed in order to calculate how distinguishing the variable is:

• ENTROPY: 

• GINI:

Now we will compare both variables for all three metrics so that we can understand them better.

For all three calculations, Humidity is proven to be a better classifier than Wind. Hence, we can confirm that all methods convey a similar story.