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Old 05-06-2011, 11:18 PM   #1
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Default New Refractometer FG Formula?

Has anyone used Sean Terrill's new refractometer formula for determining final gravities? He says that it is "on par" with the accuracy of using a hydrometer. I first learned about it on this Basic Brewing podcast episode, where he discusses the results of testing his new formula with the help of the podcast's audience. The details of the formula, along with an easy to use spreadsheet can be found here: http://seanterrill.com/2011/04/07/re...er-fg-results/

Any statistics/math people looked into this? Has anyone done their own testing of his new formula?

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Old 05-07-2011, 04:48 AM   #2
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No. I've found too much dispersion in my own experience to consider use of a refractometer for FG estimation.

Thought it was funny that he called the linear more "accurate" but a bit less "precise" than the cubic. Here's a "new new cubic" which is, in his terminology, extremely accurate (mean error 0) and equally precise (standard deviation 0.0013) as the "new cubic": FG = 0.9993 – 0.0044993*RIi + 0.011774*RIf + 0.00027581*RIi² – 0.0012717*RIf² – 0.0000072800*RIi³ + 0.000063293*RIf³. IOW all you have to do is remove the bias for perfect "accuracy".

And removing the bias leads to a better fit - reduces the mse by bias^2.

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Old 07-19-2011, 04:49 PM   #3
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AJ: Could you expand on that? If by "bias" you're referring to the zero-order coefficient, I set that to unity when doing the curve fits (not afterward) in order to hopefully improve the results that would be generated outside the interpolation ranges. If RIi = RIf = 0, then the FG result should be 1.000. You can certainly question the validity of that assumption, but I don't see how it can be compared to arbitrarily adjusting one of the coefficients after the fact.

From my perspective, the linear correlation *is* both more accurate (i.e. the mean deviation is smaller) and less precise (the standard deviation is larger). I'm entirely open to the possibility that you've noticed something I missed though.

Finally, what constitutes "too much dispersion" may be different for you than it is for others - especially given that most home brewers are apparently comfortable with hydrometers that can, at best, be read to ±0.001 SG.


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Old 07-20-2011, 01:53 AM   #4
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Originally Posted by a10t2 View Post
AJ: Could you expand on that? If by "bias" you're referring to the zero-order coefficient, I set that to unity when doing the curve fits (not afterward) in order to hopefully improve the results that would be generated outside the interpolation ranges. If RIi = RIf = 0, then the FG result should be 1.000. You can certainly question the validity of that assumption, but I don't see how it can be compared to arbitrarily adjusting one of the coefficients after the fact.
Had to go back and look at this - no idea what I was talking about at a first look. I'm pretty sure that what I had in mind is that a biased estimator (all the ones he mentions) have rms errors equal to the square root of the sum of the squares of the bias and the standard deviation squared. Thus if you have for the new cubic a mean error of 0.0007 and a standard deviation of 0.0013 the rmse will be sqrt(0.0007^2 + 0.0013^2) = 0.00148. If the estimator has 0.0007 subtracted from it (by knocking that amount off the constant term making it 0.9993 instead of 1.0000 then the mean error will be 0 and the rmse 0.0013.

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From my perspective, the linear correlation *is* both more accurate (i.e. the mean deviation is smaller) and less precise (the standard deviation is larger). I'm entirely open to the possibility that you've noticed something I missed though.
The linear estimate is the most accurate since its mean error is 0.0001 as opposed to larger values for the cubics but the cubics can be simply repaired to have 0 mean error as, of course, can the linear, by simply subtracting the mean error from the constant term. Thus they are all, with simple modification, can have the same accuracy (bias) and the rmse is totally determined by the standard deviations. As the "new cubic" and "new new cubic" have the same standard deviation they are the best with the new new being a better (in the mmse sense) estimator than the new because of the removal of the bias.

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Finally, what constitutes "too much dispersion" may be different for you than it is for others - especially given that most home brewers are apparently comfortable with hydrometers that can, at best, be read to ±0.001 SG.

I've seen discrepancies of 1 °P or more. That's enough to discourage me from using a refractometer. I can read a hydrometer to 0.1 °P and it's not that much more work (IMO).
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