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.
