Comparing variations in measurements with different scales requires standardized approaches to ensure meaningful analysis. The most common method is the Coefficient of Variation (CV), which calculates the ratio of the standard deviation to the mean (expressed as a percentage), allowing comparison across datasets with different units—for example, comparing temperature variability (°C) to rainfall variability (mm). Another approach is standardization (Z-scores), which transforms data into a common scale with a mean of 0 and standard deviation of 1, making it possible to compare variables like weight (kg) and height (cm) directly. For bounded scaling, min-max normalization rescales data to a 0–1 range, useful in machine learning.

When dealing with non-normal distributions, non-parametric methods like the Interquartile Range (IQR) or Median Absolute Deviation (MAD) are more robust than standard deviation. In cases where relative precision matters, such as lab measurements, Relative Standard Deviation (RSD) can be used. Alternatively, index-based comparisons (e.g., setting a baseline to 100) help track relative changes in different metrics, such as GDP growth versus population growth.

A key consideration is avoiding direct comparisons of raw standard deviations, as larger scales (e.g., kilometers vs. meters) can misleadingly inflate variability. Instead, CV or Z-scores provide fair comparisons. Additionally, if data contains zero or negative means, CV becomes unreliable, and normalization or Z-scores are preferable. For example, if analyzing daily stock returns (which can be negative) and temperature changes, Z-scores would be the better choice.

i don’t understand yogur question. Plis, could you explain me more?

Guillermo Becerra :

I have 4 anatomical reference lines that I want to compare their variability and select the most stable one. Because these lines measure the length between two anatomical structures to build the reference line, they vary in size between cases and also have different means (for example, the mean for one is 60 mm vs the other one 180 mm).

To be able to compare the variability, either I have to use a relative measure of variability like CV/RSD and use a test available in the cvequality package in R, or I have to standardize/normalize my data and then measure the variability using the Bartlett/Levene test and pairwise comparison using the F test.

At least that is what I think, and I am open to better solutions. Comparing the raw variability doesn't make sense, as it is evident that the lines with larger means have larger variation. Therefore, it is better to compare their relative variation.

My primary concern is that the Min/Max normalized data yields different results in the cvequality package, despite the CVs being identical to those of the raw data (That makes me hesitant to use the first solution, as I have doubts about the reliability of the cvequality R package). The other concern was Z-score standardized data has different CVs vs raw data (This part was solved as I have found out about CV's sensitivity to negative and zero values).

I wasn't sure about using the data transformation methods (solution 2) at first as I thought maybe the difference in CVs of Z-standardized vs raw is caused by changes in distribution shape.

For now, I think I have to compare CVs using the Feltz and Miller 1996 methods manually, as I cannot trust the R package, OR use Forkman J (2009) method, which is available in Medcalc and its online calculator at https://www.medcalc.org/calc/comparison_of_coefficientsofvariation.php

Abdulhamid Dehghani :

I agree that I should not use raw data comparison, as larger numbers have naturally larger variability.

I chose Min/Max normalization because it yields the same CV as raw data, which has no negative values (unlike Z-score standardization), thereby not affecting the CV.

Jochen Wilhelm

I thought that both z-score and min/max methods preserve the distribution's shape and do not affect the Levene test. Can you elaborate on why using min/max normalization is a bad idea (I am not so much of an expert in stats, so I apologize if it looks like a simple question that I should know)