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Calculating Percentage Errors

Date: 02/20/99 at 17:40:01
From: Brandy
Subject: Error calculation

I need to know how to calculate percent error from a set of data. The 
data include predicted values and observed values. How do I basically 
determine percent error?


Date: 02/21/99 at 06:28:41
From: Doctor Mitteldorf
Subject: Re: Error calculation

The surefire way is to do your calculation twice, once for a maximum 
and once for a central value. For example

(3 +/- 0.1) + (7 +/- 0.1) / (0.9 +/- 0.1)

First you do the central value:  (3+7)/.9 = 11.1

Then you get a high value. Do this by choosing the HIGHEST value in 
the numerator and the LOWEST in the denominator:

(3.1+7.1)/0.8 = 12.75

So, you'd quote the result as 11.1 +/- 1.6


There are more sophisticated ways to approach this, too. For any 
numbers that add or subtract, you can add their absolute errors. For 
any numbers that multiply or divide, you can add their percentage 
errors and then turn them back to absolute errors at the end.

Another variation: if the errors in the different constituent numbers 
are independent, it may be justifiable to add them "quadratically" as 
the square root of the sum of the squares, rather than as the straight 
sum. The meaning of this is, essentially, that if you have a lot of 
numbers you are adding up, it is unlikely that you erred to the high 
side on all of them. Rather, you can expect some cancellation in the 
errors, so the uncertainty in the end is not as great. For example,

(2 +/- .1) + (3 +/- .1) - (4 +/- .2)

The central value is 2 + 3 - 4 = 1

The error is sqrt(.1^2 + .1^2 + .2^2) = .24

You should quote the answer as 1.0 +/- .24 

- Doctor Mitteldorf, The Math Forum   
Associated Topics:
High School Statistics

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