Kendall's W for testing similarity of proportions for non-ranked count data?


New Member
Hello forum,

I can't find the answer to this anywhere, and I'd really appreciate a helping hand. :confused:

I'm doing an MSc project and my supervisor has told me I need to use a Kendall's tau to compare conformity of non-ranked count data across a set of case studies.

To explain further:

I am using a framework to assign categories to a set of 17 species case studies. My data are arranged in the form of a contingency table with species 1-17 as columns and categories 1-18 as rows. The cells in the table are filled in with the number of each type of category assigned to each species. Cells can have values of 0, and columns and rows will not add up to equal totals.

This is an illustration of how my data will look, using some random values:

The idea is to compare proportions of each category total between species and identify whether there is an overall concordance and similarity between category proportions.

My uni supervisor suggested Kendall's tau, but having googled it, it seems this is not suitable for comparing more than 2 cases. So Kendall's W would be more suitable, according to my google sleuthing.

However, it also seems that both Kendall's tau and Kendall's W are only suitable for rank data, (a.k.a. ordinal). This troubles me as my data are not ordinal!

Does anyone know if Kendall's W will still be useful? Or was I advised to do the wrong type of test here?

Thank you for reading this - any help would be much appreciated!



TS Contributor
Hi Kate,

Although I'm not particularly familiar with Kendall's W, most non-parametric analyses in specialized software rank the raw data before the process, so it can be done with any scale (except for nominal /binary data), so I wouldn't see any problem with the scale in your case.

On the other hand, I think Biplots can also be very useful, particularly if you want to detect categories/species that behave similarly. Biplots are multivariate graphs that can be used to detect clusters in observations or relationships within the variables. Correspondence Analysis, which is actually some form of Biplot for contingency tables, could be of use, maybe you could read a bit about it to know whether your objectives agree with the idea.

Hope to help a bit, regards