Andres and Marzo's delta

In statistics, Andrés and Marzo's Delta is a measure of an agreement between two observers used in classifying data. It was created by Andres & Marzo in 2004.[1]

Rationale for use

The most commonly used measure of agreement between observers is Cohen's kappa. The value of kappa is not always easy to interpret and it may perform poorly if the values are asymmetrically distributed. It also requires that the data be independent. The delta statistic may be of use when faced with the potential difficulties.

Mathematical formulation

Delta was created with the model of a set of students (C) having to choose correct responses (R) from a set of n questions each with K alternative answers. Then

{\frac {K\Sigma _{ii}-n}{n(K-1)}}

where the sum is taken over all the answers ( x_ij ) and x_ii are the values along the main diagonal of the C x R matrix of answers.

This formula was extended to more complex cases and estimates of the variance of delta were made by Andres and Marzo.

Uses

It has been used in a variety of applications including ecological mapping[2] and alien species identification.[3]

References

Andrés, A Martín; Marzo, P. Femia (2004) "Delta: a new measure of agreement between two raters". British Journal of Mathematical and Statistical Psychology, 57(1):1–19 doi:10.1348/000711004849268
Ellis EC, Wang H (2006) "Estimating area errors for fine-scale feature-based ecological mapping". International Journal Remote Sensing, 27(21), 4731–4749 doi:10.1080/01431160600735632
Prinzing A, Durka W, Klotz S, Brandl R (2005) "How to characterize and predict alien species? A response to Pysek et al. (2004)", Diversity and Distributions, 11 (1), 121–123 doi:10.1111/j.1366-9516.2005.00138.x

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[1] Andrés, A Martín; Marzo, P. Femia (2004) "Delta: a new measure of agreement between two raters". British Journal of Mathematical and Statistical Psychology, 57(1):1–19 doi:10.1348/000711004849268

[Ellis2006-2] Ellis EC, Wang H (2006) "Estimating area errors for fine-scale feature-based ecological mapping". International Journal Remote Sensing, 27(21), 4731–4749 doi:10.1080/01431160600735632

[Prinzing2005-3] Prinzing A, Durka W, Klotz S, Brandl R (2005) "How to characterize and predict alien species? A response to Pysek et al. (2004)", Diversity and Distributions, 11 (1), 121–123 doi:10.1111/j.1366-9516.2005.00138.x