Cohen's Kappa

This function computes the Cohen's kappa coefficient
Cohen's kappa coefficient is a statistical measure of inter-rater reliability. It is generally thought to be a more robust measure than simple percent agreement calculation since k takes into account the agreement occurring by chance. Kappa provides a measure of the degree to which two judges, A and B, concur in their respective sortings of N items into k mutually exclusive categories. A 'judge' in this context can be an individual human being, a set of individuals who sort the N items collectively, or some non-human agency, such as a computer program or diagnostic test, that performs a sorting on the basis of specified criteria. The original and simplest version of kappa is the unweighted kappa coefficient introduced by J. Cohen in 1960. When the categories are merely nominal, Cohen's simple unweighted coefficient is the only form of kappa that can meaningfully be used. If the categories are ordinal and if it is the case that category 2 represents more of something than category 1, that category 3 represents more of that same something than category 2, and so on, then it is potentially meaningful to take this into account, weighting each cell of the matrix in accordance with how near it is to the cell in that row that includes the absolutely concordant items. This function can compute a linear weights or a quadratic weights.
Syntax: kappa(X,W,ALPHA)

Inputs:
X - square data matrix
W - Weight (0 = unweighted; 1 = linear weighted; 2 = quadratic
weighted; -1 = display all. Default=0)
ALPHA - default=0.05.

Outputs:
- Observed agreement percentage
- Random agreement percentage
- Agreement percentage due to true concordance
- Residual not random agreement percentage
- Cohen's kappa
- kappa error
- kappa confidence interval
- Maximum possible kappa
- k observed as proportion of maximum possible
- k benchmarks by Landis and Koch
- z test results

Example:

x=[88 14 18; 10 40 10; 2 6 12];

Calling on Matlab the function: kappa(x)

Answer is:

UNWEIGHTED COHEN'S KAPPA

Observed agreement (po) = 0.7000
Random agreement (pe) = 0.4100
Agreement due to true concordance (po-pe) = 0.2900
Residual not random agreement (1-pe) = 0.5900
Cohen's kappa = 0.4915
kappa error = 0.0549
kappa C.I. (alpha = 0.0500) = 0.3839 0.5992
Maximum possible kappa, given the observed marginal frequencies = 0.8305
k observed as proportion of maximum possible = 0.5918
Moderate agreement
Variance = 0.0031 z (k/sqrt(var)) = 8.8347 p = 0.0000
Reject null hypotesis: observed agreement is not accidental

Created by Giuseppe Cardillo
giuseppe.cardillo-edta@poste.it

To cite this file, this would be an appropriate format: Cardillo G. (2007) Cohen's kappa: compute the Cohen's kappa ratio on a 2x2 matrix.
http://www.mathworks.com/matlabcentral/fileexchange/15365