Galtung (1967) introduced the AJUS system as a way to classify distributions according to shape. This is a means to reduce complexity. The underlying idea is to classify distributions by ignoring small differences that are not important. The system was originally developed for eye-balling, but having it done by a computer makes the classification more systematic.

All distributions are classified as being one of AJUS, and I have added a new type “F” to complement the ones identified by Galtung.

- A: unimodal distribution, peak in the middle
- J: unimodal, peak at either end
- U: bimodal, peak at both ends
- S: bimodal or multi-modal, multiple peaks
- F: flat, no peak; this type is new

The skew is given as -1 for a negative skew, 0 for absence of skew, or +1 for a positive skew. The skew is important for J-type distributions: it distinguishes monotonous increase from monotonous decrease.

I have implemented the AJUS system in my R package agrmt. By setting the tolerance, we can determine what size of differences we consider small enough to be ignored. The default tolerance is 0.1, equivalent to 10% if using 0 to 1. AJUS implemented in R sets a systematic threshold, something we do not do when eye-balling differences.

The tolerance parameter is not a trivial choice, but a test is included in the R package to directly test sensitivity to the tolerance parameter (ajusCheck).

Here are some examples (using the experimental ajusPlot function and tolerance = 10):

Differences smaller than the tolerance set (10) are ignored.

Reference: Galtung, J. 1969. Theory and Methods of Social Research. Oslo: Universitetsforlaget.

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More recent versions of the agrmt package offer AJUSFL by default, but include an option to use Galtung’s AJUS strictly. In the modified version, J-type and L-type distributions are differentiated clearly (top-left and bottom-right in the graph of the original post respectively). The strict version only offers AJUS as options; the F-type distribution is not recognized as one.