# How to interpret Ratkowsky-Lance index (clustering)

I'm conducting an hierarchical cluster analysis of binary variables in SPSS (Complete-linkage clustering with Sokal and Sneath 1 as the distance measure). For guidance on the number of clusters to use, I'm using the Ratkowsky-Lance index, which is recommended for binary variables. (I'm using the macros that @ttnphns has awesomely published.)

However, the index is always higher for higher numbers of clusters. I've tested 2 to 20 clusters and the index just increases with each additional cluster. I thought one should simply choose the highest index, but that can't be the case, right? Am I rather supposed to interpret the plot more like a scree plot, looking for the elbow / inflexion point?

Many thanks!

• The formula used in the macro was mean[sqrt(B/T)] (see the dcumentation). This formula is often found in papers, and probably in packages (be it R or other language). I found it inadequate. Some papers cite another formula, mean[sqrt((B/k)/T)] = mean[Eta/sqrt(k)], where k is the number of clusters and, Eta is the Eta statistic of ANOVA. That formula is better and is what (surely, as I can say) the inventors arrived finally at. – ttnphns Jun 16 '17 at 20:20
• (cont.) The new SPSS macro of the criterion using this formula, and also allowing to process nominal and quantitative variables at once, has been prepared and tested by me. It is to be uploaded very soon. Meanwile, drop me email (find it on my web-page) and I'll send the new macro to you back. – ttnphns Jun 16 '17 at 20:20