Leik’s Measure of Ordinal Consensus

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.
leik1

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.

One thought on “Leik’s Measure of Ordinal Consensus

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s