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76 3 Data Clusterine

where P(A) is the proportion of times the k judges agree and P(E) is the proportion
of times that we would expect the k judges to agree by chance. If there is complete
agreement among the judges, then el (P(A)=l, P(E)=O). If there is no agreement
among the judges other than what would be expected by chance, then GO
(P(A)=P(E)). The values of P(A) and P(E) are computed as follows:

For the Rocks example these quantities are computed as P(A)=0.971 and
P(E)=0.418, resulting in a high value of K, ~=0.95. In order to test the significance
of K, the following statistic, approximately normally distributed for large n with
zero mean and unit standard deviation, is used:

The value of z = 9.5 is obtained for the present example, allowing us to conclude
significantly high agreement at a a= 0.01 significance level (zeo.ol = 2.32).

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