# How to calculate for significant difference between Cohen's Kappa values?

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Leonard Hickman on 6 Sep 2021
Answered: Jeff Miller on 14 Sep 2021
I have calculated the Cohen's Kappa value determining agreement between Test A and Test B, as well as Cohen's Kappa for agreement between Test A and Test C. What method would I use to calculate for a significant difference in Kappa values between agreement for A-B compard to A-C? Are there any existing scripts/functions available for this?
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Leonard Hickman on 13 Sep 2021
Two separate samples, one sample that underwent tests A & B and one sample that underwent tests A & C.

Star Strider on 6 Sep 2021
Edited: Star Strider on 13 Sep 2021
I used Cohen’s κ many years ago. From my understanding, from reading Fliess’s book (and correspoinding with him), Cohen’s κ is normally distributed. An excellent (in my opinion) and free resource is: Interrater reliability: the kappa statistic . There are others, although not all are free.
EDIT — (13 Sep 2021 at 10:58)
To get p-values and related statistics for normally-distributed variables, the ztest function would likely be appropriate.
.

Ive J on 12 Sep 2021
You can build confidence intervals around your Kappa values, and then see if they overlap.
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Ive J on 13 Sep 2021
You may want to take a look at this thread. Then you can calculate the z-score and get a p-value out of this.
pval = 2*normcdf(zvalue, 'upper'); % two-sided test

Jeff Miller on 14 Sep 2021
As I understand it, the fundamental question is whether tests A & B agree better than tests A & C, beyond a minor improvement that could just be due to chance (or agree worse, depending on how the tests B and C are labelled). The null hypothesis is that the agreement between A & B is equal to the agreement between A & C.
The most straightforward test for this case is the chi-square test for independence. Imagine the data summarized in a 2x2 table like this:
% Tests agree Tests disagree
% A & B group: 57 17
% A & C group: 35 8
with total N's of 74 in the first group and 43 in the second group. MATLAB's 'crosstab' command will compute that chi-square test for you. See this answer for an explanation of how to format the data and run the test.
Cohen's Kappa is a useful numerical measure of the extent of agreement, but it isn't really optimal for deciding whether the levels of agreement are different for the two pairs of tests.

R2021a

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