Re: Comparisons using RMS Error and Correlation

Nicholas Kinar wrote:
I have two datasets that have been collected in the context of snow science.
Both datasets contain esimates of Snow Water Equilivant (SWE), which is a
measure of the amount of water that remains when snow on the ground surface
in a particular area is melted down, thereby giving a measurement of the
equilivant depth of water (i.e. 20 mm). Dataset A consists of observations
made with Instrument #1, whereas Dataset B consists of observations made
with Instrument #2. To compare the datasets, I plot dataset A on the x-axis
and dataset B on the y-axis, and then calculate the correlation coefficient
to determine how well the relationship between the datasets can be described
by a linear model. I do this for two separate research sites, Site #1 and
Site #2. Thus, I have one graph of the correlations for Site #1, and
another graph of the correlations for Site #2. Suppose that the correlation
coefficient is r^2 = 0.86 for Site #1, and the correlation coefficient is
r^2= 0.79 for Site #2. However, when I calculate the Root Mean Squared
Error for both sites, I find that RMS = 12.65 mm for Site #1, and RMS = 6.23
mm for Site #2. Why is the RMS greater for Site #1 (which has a higher
correlation), whereas the RMS is lower for Site #2 (which has a lower
correlation)?

Thank you ever so much for your time and assistance.

Nicholas

Correlation ignores differences in mean and s.d., but RMS includes
them, and also depends on the overall level of variability:

RMS = sqrt[(mA - mB)^2 + (sA - sB)^2 + 2*sA*sB*(1 - rAB)].

.

Relevant Pages

  • Re: Comparisons using RMS Error and Correlation
    ... Both datasets contain esimates of Snow Water Equilivant, ... measure of the amount of water that remains when snow on the ground surface ... and dataset B on the y-axis, and then calculate the correlation coefficient ... Why is the RMS greater for Site #1 (which has a higher ...
    (sci.stat.math)
  • Comparisons using RMS Error and Correlation
    ... I have two datasets that have been collected in the context of snow science. ... Both datasets contain esimates of Snow Water Equilivant, ... measure of the amount of water that remains when snow on the ground surface ... and dataset B on the y-axis, and then calculate the correlation coefficient ...
    (sci.stat.math)
  • Re: Comparisons using RMS Error and Correlation
    ... Both datasets contain esimates of Snow Water Equilivant, ... measure of the amount of water that remains when snow on the ground surface ... and dataset B on the y-axis, and then calculate the correlation coefficient ... unaffected by adding a constant to the predictor, ...
    (sci.stat.math)
  • Re: Comparisons using RMS Error and Correlation
    ... Both datasets contain esimates of Snow Water Equilivant, ... measure of the amount of water that remains when snow on the ground ... and dataset B on the y-axis, and then calculate the correlation ... Why is the RMS greater for Site #1 (which has a higher ...
    (sci.stat.math)
  • Re: Comparisons using RMS Error and Correlation
    ... Nicholas Kinar wrote: ... -- Reef Fish Bob. ... and dataset B on the y-axis, and then calculate the correlation ... Why is the RMS greater for Site #1 (which has a higher ...
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