# Test for Statistical Differences Among Coefficients of Variation (using R)?

I have two datasets, and I wish to determine the statistical difference between two groups. I am comparing a visual plant injury scoring system to a remotely-sensed scale, and the coefficient of variation (CV) is usually used for this purpose (it goes on the assumption that the lower the CV of the dataset, the "better" the scale). It's important to note that the data has been normalized between 0 and 1, to make for a more accurate comparison.

How can I test for differences in the two CVs? Given there are just two datasets, it would be easy to do a t-test if comparing means. However, I'm not needing to compare the means. Can this be done in R?

Here is the data, in case reference is needed:

dataset <- data.frame(visual = c(152,
150,
275,
407,
364,
105,
415,
221,
374,
408,
265,
290,
186,
130,
263,
113,
290,
157,
348,
384,
369,
175,
421,
183,
214,
146,
333,
374,
201,
262,
364,
343,
395,
332,
290,
294),
remotesense = c(104,
132,
148,
370,
257,
373,
409,
320,
350,
178,
236,
100,
219,
403,
107,
345,
102,
307,
292,
258,
271,
220,
165,
211,
204,
420,
339,
380,
227,
390,
354,
153,
423,
103,
342,
116))

• I don't understand how a CV (presumably coefficient of variation, which is a description of a univariate dataset) could be used to compare two measurement systems (a bivariate problem). Could you explain? – whuber Nov 19 '19 at 22:21
• @whuber yes, absolutely. Normally, it shouldn't be if you have two completely different measurement systems, but these datasets were normalized between 0 and 1, which does allow for similar comparisons to be made. Normalization was made with the formula that can be found here: stats.stackexchange.com/questions/70801/… – ihb Nov 19 '19 at 22:26
• I still don't get it: comparing two univariate statistics tells us almost nothing about how the two datasets compare. You need to perform some kind of calibration or regression analysis to accomplish that. – whuber Nov 20 '19 at 15:29