A psychologist has developed a test for school children that

A psychologist has developed a test for school children that is supposed to identify who will commit violent crimes during adolescence and young adulthood. In one school 10 percent of the 200 children tested show a positive result, indicating criminal potential. Half of these children do indeed go on to commit violent crimes, whereas only 5 percent of those who tested negative do so. 1. What is the observed agreement between the test and the result? 2. What is the expected agreement between the test and the result? 3. Calculate the kappa statistic to measure how well the test result agrees with the outcome.

Solution

A psychologist has developed a test for school children that is supposed to identify who will commit violent crimes during adolescence and young adulthood. In one school 10 percent of the 200 children tested show a positive result, indicating criminal potential. Half of these children do indeed go on to commit violent crimes, whereas only 5 percent of those who tested negative do so.

1. What is the observed agreement between the test and the result?

Observed agreement = (10+171) / 200 = 0.905

2. What is the expected agreement between the test and the result?

Expected agreement = (1.9+162.9) / 200 = 0.824

3. Calculate the kappa statistic to measure how well the test result agrees with the outcome.

Kappa = (0.905 - 0.824) / (1-0.824) = 0.46

T+

T-

C+

10

9

19

C-

10

171

181

20

180

200

Expected Frequencies

Total

1.9

17.1

19

18.1

162.9

181

Total

20

180

200

\\

Observed agreement = (10+171) / 200 = 0.905

Expected agreement = (1.9+162.9) / 200 = 0.824

Kappa = (0.905 - 0.824) / (1-0.824) = 0.46