What is the RMSE normalized by the mean observed value called?

Question

I have been using the Root Mean Squared Error (RMSE) to measure the accuracy of values predicted using a model. I understand that the value returned is using the units of my measures (rather than a percentage). However, I would like to quote my values as a percentage. The approach that I have taken is to normalize the RMSE by the mean value of my observations.

Is there a term for RMSE/mean ?

score 14 · Accepted Answer · edited Apr 13 '17 at 12:44

14

Yes, it is called the coefficient of variation. See this question for some discussion about this parameter, or read the Wikipedia entry.

edited Apr 13 '17 at 12:44

Community

1

answered Apr 21 '12 at 01:39

Dilip Sarwate

41,202
4
94
200

3

+1. Isn't also called: relative root mean square error (rRMSE)? , cc/ @celenius. – Andre Silva Jan 30 '14 at 11:28

score 2 · Answer 2 · answered Apr 21 '12 at 10:39

In my field (analytical chemistry), absolute error / absolute value = relative error, so relative RMSE [at mean x] would be understood easily.

I'd clarify that the value I divide by is the average, as often the relative error at the extreme values is used:

error specification of measuring instruments often is relative error at maximum value
in (chemical-analytical) calibration the relative error at the limit of quantitation or the lower limit of the actual calibration is important.

I'm not sure if there is a standard term in my field, so I will probably use `relative error` as it sounds a little more self-explanatory. — celenius, Apr 21 '12 at 13:37

score 2 · Answer 3 · edited Jun 19 '19 at 11:53

2

It is called Normalised Root Mean Square Error (nRMSE) or Relative Root Mean Square Error (rRMSE). You can use either mean or range as the denominator. Read the Wikipedia article

edited Jun 19 '19 at 11:53

Dan Scally

228
2
13

answered Mar 12 '18 at 13:20

calculus

21
3

What is the RMSE normalized by the mean observed value called?

3 Answers3