# Coefficient of Variance(clarification)

1. Aug 9, 2012

### mattkunq

Can someone please help me with this. I read on wikipedia that the coefficient of Variance can be used when the measurements are of ratio scales but cannot be used on interval scales.

I know it is useful to use it to compare samples with completely units like the variance in your mass measurement variation to your volume measurements.

The part i am confused about is whether the follow is alright.
So lets say I have 2, 6 sided dice that is rigged to fall on 6 more. So i roll it a lot and i get a distribution of the sumed values, the sample mean will be lets say x1 with sample variance S1.

now if i were to relabeled those dice so that it falls one 1 more than the new sample mean would be x2 but the sample variance would stay the same, ie the width of the normal distrubition does not change.

So based on this i would think taking a Coefficient of variance which is defined as the sample variance divided by the sample mean would be wrong representation of the variation of the dice to compare with other non related experiments ie (variance in drawing from two decks of cards )

the Coefficient of Variance of X1 will not equal to that of X2 making a variance comparison to other non related experiments kinda meaningless as the coefficient of variance depend so much on the mean.

2. Aug 18, 2012

### Stephen Tashi

Is that really true in general?

3. Aug 19, 2012

### mattkunq

If I added 1 a constant number same for every side to every side of the dies then ya i would think so.

4. Aug 20, 2012

### Stephen Tashi

But you didn't say you were adding a constant, you said "relabel".

I think the coefficient of variation is primarily useful for random variables whose values are physical properties whose units-of-measurement does not involve an additive constant. Many physical properties like length, mass etc. are measured in units where "conversion factors" are used to convert from one type of unit to another. I agree that the coefficient of variation is rather meaningless for phenomena where there is a arbitrary additive constant involved.

5. Aug 21, 2012

### mattkunq

Ok,
So Im doing a project on the variation of a black and white picture and I quantify that by calculating the COV% for the grey level. I noticed that when the sample is darker the COV% tends to be a larger number than a whiter image. Even if its the same image but different colors.

So my question is is it ok to compare COV% between very dark images and very light images or would be it be better to compare just the Stdev. The grey scale is from 0 to 255 with 255 as brightest ie white.

6. Aug 21, 2012

### Stephen Tashi

I can't guess the answer to that unless I know why you're comparing them. A statistic by itself is neither good nor bad. It is only good or bad relative to what decisions will be made by people who use it. It' may also be important whether we must answer the question for any possible random image of anything that might be taken or whether the population is more restricted - such as satellite images of The Mouth Of Wilson, VA.

7. Aug 21, 2012

### mattkunq

What I am looking for is the comparison in Mottle in the pictures. How the grey level varies in the picture from one to another. And being able to say which one will be better to the human eye.

8. Aug 22, 2012

### Stephen Tashi

My understanding of the technical definition of "mottle" in an image is that it is a localized unevenness in the image. If that is what you're trying to compare, I don't think a statistic that is only a function of the histogram of pixel intensities over the entire image will be useful. I think neither the standard deviation nor the coefficient of variation will be useful.

9. Aug 22, 2012

### mattkunq

how come not? =S

10. Aug 22, 2012

### Stephen Tashi

Just consider a one dimensional example. If you histogram the numbers
1,2,3,4,5,6,7,8 you get the same answer as if you histogram the numbers 0,8,1,7,2,6,3,5,4 which has more uneven transitions.

11. Aug 22, 2012

### mattkunq

Ok i dun just take the the stdev and cov, I fourier transform it and do it a bandpass filter for the different sizes of mottle. then i reverse transform it and i calculate the cov of the filtered image. With only blobs or certain sizes and no gradients or minimal