The likelihood ratio statistic.

Figure 5.1 illustrates the coverage of the classification rules R1, R2, and R3.

Determine which is the best and worst rule according to:

There are 29 positive examples and 21 negative examples in the data


set. R1 covers 12 positive examples and 3 negative examples. The


expected frequency for the positive class is 15 × 29/50 = 8.7 and the


expected frequency for the negative class is 15×21/50 = 6.3. Therefore,


the likelihood ratio for R1 is





R2 covers 7 positive examples and 3 negative examples. The expected


frequency for the positive class is 10 × 29/50 = 5.8 and the expected


frequency for the negative class is 10 × 21/50 = 4.2. Therefore, the


likelihood ratio for R2 is





R3 covers 8 positive examples and 4 negative examples. The expected


frequency for the positive class is 12 × 29/50 = 6.96 and the expected


frequency for the negative class is 12 × 21/50 = 5.04. Therefore, the