I am performing cluster analysis (k-means and hierarchical) based on multiple variables. Each variable is in percentage 0-100% and the sum of all variables is at most 100%.
I see that in many of the cluster analysis guides such as this one https://www.statmethods.net/advstats/cluster.html it is suggested to "rescale variables for comparability". I understand that this applies in the case where you have for example variables expressed in Kg and others in meters, which can be orders of magnitude different. This nice answer on SO https://stackoverflow.com/questions/5648383/how-to-apply-a-hierarchical-or-k-means-cluster-analysis-using-r explains that "scale (standardise) the data to allow each variable to be compared on a common scale. With data measured in different "units" or on different scales (as here with different means and variances) this is an important data processing step if the results are to be meaningful or not dominated by the variables that have large variances"
In my case I have the same units but should I also consider the variance of each variable as to determine if I should scale my data? Is it a good idea to standardize the data even if it's in the same units?