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Cohen's kappa is used to compare the degree
of consensus between raters (inspectors)
in, for example, Measurement Systems Analysis.
It uses a contingency table approach.
Two raters inspect 150 parts independently
and make the following determinations:
| |
|
|
Bret |
|
| |
|
Reject |
Accept |
Total |
| |
Reject |
20 |
19 |
39 |
| Alice |
Accept |
1 |
110 |
111 |
| |
Total |
21 |
129 |
150 |
The expected values in each cell would
be:
| |
|
|
Bret |
|
| |
|
Reject |
Accept |
Total |
| |
Reject |
5.46 |
33.54 |
39 |
| Alice |
Accept |
15.54 |
95.46 |
111 |
| |
Total |
21 |
129 |
150 |
These are the values that would give the
same totals if the determinations were made
by pure chance and is calculated from:
(row total x column
total)/overall total
The Kappa statistic is calculated from:
where:
| Actual |
the number of times
the appraisers agreed (110 + 20 = 130) |
| Expected |
the number of times
they would have agreed by chance (5.46
+ 95.46) |
| Trials |
the number of trials |
The value of Kappa will be between 0 and
1.
If the results were made by chance, neither
rater showing judgment the value would be
zero. If the raters were in perfect agreement,
the number of agreements would equal the
number of trials and Kappa would be 1.
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