In 1966 Robert K. Leik introduced a measure of ordinal consensus based on cumulative frequency distributions. It can be used to express agreement or polarization, just like Cees van der Eijk‘s measure of agreement “A”, and its derived measure of polarization. A difference exists in that in Leik’s measure, an equal distribution of frequencies – all categories equally common – does not always give the same value. Leik defends this, arguing that an equal distribution should only be considered the mid-point between agreement and polarization if the number of categories is very large. With a small number of categories, polarization may simply be a result of chance.
Here’s a graphical summary of how Leik’s measure of ordinal dispersal behaves with increasing numbers of categories (consensus is defined as 1 minus dispersal), as outlined in table 3 of the article.
Leik’s measure of ordinal dispersion is available in the latest version of the package agrmt (version 0.27, not yet on CRAN)
Leik, R. 1966. ‘A measure of ordinal consensus’. Pacific Sociological Review 9 (2): 85–90.
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