Error Propagation Made Easy
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Error Propagation Calculus
Human Biology and Physiology Chronic Pain and Individual Differences in Pain Perception Pain-Free and Hating error propagation khan academy It: Peripheral Neuropathy Neurotransmitters That Reduce or Block Pain Load more EducationScienceBiologyThe Concept of Error Propagation The Concept of Error Propagation Related Book error propagation average Biostatistics For Dummies By John Pezzullo A less extreme form of the old saying "garbage in equals garbage out" is "fuzzy in equals fuzzy out." Random fluctuations in one or more measured variables produce random fluctuations in anything you http://pubs.acs.org/doi/pdf/10.1021/ed1004307 calculate from those variables. This process is called the propagation of errors. You need to know how measurement errors propagate through a calculation that you perform on a measured quantity. Here's a simple way to estimate the SE of a variable (Y) that's calculated from almost any mathematical expression that involves a single variable (X). Starting with the observed X value (Xo), and its standard error (SE), just do the following 3-step calculation: Evaluate the expression, substituting http://www.dummies.com/education/science/biology/the-concept-of-error-propagation/ the value of Xo - SE for X in the formula. Call the result Y1. Evaluate the expression, substituting the value of Xo + SE for X in the formula. Call the result Y2. The SE of Y is simply (Y2 - Y1)/2. Here's an example that shows how (and why) this process works. Suppose you measure the diameter (d) of a coin as 2.3 centimeters, using a caliper or ruler that you know (from past experience) has an SE of ± 0.2 centimeters. Now say that you want to calculate the area (A) of the coin from the measured diameter. If you know that the area of a circle is given by the formula you can immediately calculate the area of the coin as which you can work out on your calculator to get 4.15475628 square centimeters. Of course, you'd never report the area to that many digits because you didn't measure the diameter very precisely. So just how precise is your calculated area? In other words, how does that ± 0.2-centimeter SE of d propagate through the formula to give the SE of A? One way to answer this question would be to consider a margin of error (ME) around the observed diameter (d) that goes from one SE below d to one SE above d. The ME is always two SEs wide. In the coin exampl
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