Agreement measures summarize the similarity of the results of two binary or
Asymmetric agreement measures are dependent on the assignment of X and Y variables. They are
often useful due to the natural interpretation as the proportion of the comparative method (X)
results in which the new method (Y) results are the same.
For a binary test, with positive/negative results, the results can be expressed as a 2x2
Symmetric agreement measures are not affected by interchanging the X and Y variable. These
are useful in many other cases, such as comparing observers, laboratories, or other factors
where neither is a natural comparator. There are various measures based on the mean of the
proportions to which X agrees with Y, and Y agrees with X. The Kulczynski, Dice-Sørensen, and
Ochiai are three such measures that use arithmetic, harmonic, and geometric mean of the
The harmonic mean weights the smaller proportion more heavily and produces the smallest value
amongst the three measures. The geometric mean is the square root of Bangdiwala’s B statistic,
which is the ratio of the observed agreement to maximum possible agreement in the agreement
plot. The arithmetic mean has the greatest value. In most cases, of moderate to high
agreement, there is very little to choose between the measures.
The overall proportion of agreement is the sum of the diagonal entries divided by the