Average Deviation

The average deviation (AD) is used as a measure of dispersion or within-group interrater agreement and may be referred to as the average absolute deviation or mean deviation. The average deviation is often defined in one of two ways: by deviations from the mean (ADM) or by deviations from the median (ADMd). The average deviation is calculated by taking the difference between each score and the mean (or median), summing the absolute values of these deviations, and then dividing the sum by the number of deviations. As a measure of dispersion, the larger the AD, the greater is the variability in a distribution of scores. As a measure of within-group interrater agreement, the larger the AD, the greater is the disagreement among raters evaluating a single target on a categorical rating scale.

The formula for the computation of the average deviation using the mean is

where

Σ directs you to add together what follows it,

X is each individual score in the distribution of scores,

X¯ is the mean,

the vertical lines are the absolute value symbols and direct you to disregard the fact that some deviations are positive and some negative, and

n is the number of cases or number of raters.

The formula for the computation of average deviation using the median (ADMd) would substitute the median for the mean in the above equation.

More about the average deviation as a measure of dispersion:

• It gives equal weight to the deviation of every value from the mean or median.
• The average deviation from the median has the property of being the point at which the sum of the absolute deviations is minimal compared with any other point in the distribution of scores.
• Given that the AD is based on every value in the distribution of scores, it provides a better description of the dispersion than does the range or quartile deviation.
• In comparison with the standard deviation, the AD is less affected by extreme values and easier to understand.

More about the average deviation as a measure of within-group interrater agreement:

• The AD provides an index of interrater agreement in the metric (measurement units) of the original rating scale.
• A statistically derived cutoff for an acceptable level of disagreement in raters' evaluations of a single target is c/6values, where c is the number of response options or rating categories. Values of AD exceeding this cutoff value (e.g., values of AD exceeding a cutoff value of 1.2 on a 7-point rating scale) would indicate disagreement among raters, and values of AD below the cutoff would indicate agreement in raters' scores of the single target.
• In comparison with other measures of withingroup interrater agreement, including the standard [Page 67]deviation, the AD index is easiest to understand and interpret.