This is generally used to describe a family of measures of dispersion, i.e. of the spread of values for a variable in a dataset.

I have gained hugely from the Wikipedia article “Average absolute deviation” and I recommend that if you want to get your head around all of this topic but the reality is that in my experience these measures rarely come up in therapy research or reports where the most common measure of dispersion reported is the standard deviation or sometimes its square, the variance. Read on if you want the gory details!

Although the family of average absolute deviation measures are generally used to measure deviation from the central location of a dataset, the same measurements can also be used to summarise the range of error in measurements of something when the correct answer is known when they become a family of ways of assessing unreliability of measurement. (And in that situation the average deviation, rather than the average absolute deviation indicates invalidity of measurement: the bias in the measurements.)

#### Details #

The one statistic within this family was the mean absolute deviation from the mean but I think I’ve only ever encountered that in statistics textbooks or papers not in reports. The full family involves two things: an average of the absolute deviations, in the mean absolute deviation from the mean that average is the mean. The other aspect is about the absolute deviations from what measure of central location in the data. To make things a bit confusing, in the mean absolute deviation from the mean that measure of central location is again the mean, hence the name: “mean absolute deviation from the mean”! The range of options is:

* for the average of the deviations:

the mean

the median

* and for the central location in the data from which the deviations are calculated:

the mean

the median

the mode (seems a terrible idea to me!)

or even the mean of the range, i.e. the value halfway between the minimum and maximum in the data

I could add a fair bit more about these measures and how different choices of average of the absolute deviations and/or of measure of central tendency can lead to rather different values. Perhaps more usefully I will add something about the relationship between the various options and the standard deviation … but those are to come!

#### Try also #

Bias

Dispersion

Mean

Median

Mode

Range

Reliability

Standard deviation

Validity

Variance: introduction

Variance: computation and bias

#### Chapters #

The topic could have come into Chapter 5 but that would have been crazy use of our word limit given that I think I’ve never seen these statistics reported in MH/therapy work!

#### Online resources #

None yet.

#### Dates #

First created 21.iii.24.