Propagation Error Subtraction
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Error Propagation Physics
for Simple Expressions Related Book Biostatistics For Dummies By John Pezzullo Even though some general error-propagation formulas are very complicated, the rules for error propagation average propagating SEs through some simple mathematical expressions are much easier to work with. Here are some of the most common simple rules. All the rules that involve two or more variables assume that those variables have been measured independently; error propagation square root they shouldn't be applied when the two variables have been calculated from the same raw data. Adding or subtracting a constant doesn't change the SE Adding (or subtracting) an exactly known numerical constant (that has no SE at all) doesn't affect the SE of a number. So if x = 38 ± 2, then x + 100 = 138 ± 2. Likewise, if x = 38 ± 2, then x - 15 = 23 ± 2. Multiplying (or
Error Propagation Chemistry
dividing) by a constant multiplies (or divides) the SE by the same amount Multiplying a number by an exactly known constant multiplies the SE by that same constant. This situation arises when converting units of measure. For example, to convert a length from meters to centimeters, you multiply by exactly 100, so a length of an exercise track that's measured as 150 ± 1 meters can also be expressed as 15,000 ± 100 centimeters. For sums and differences: Add the squares of SEs together When adding or subtracting two independently measured numbers, you square each SE, then add the squares, and then take the square root of the sum, like this: For example, if each of two measurements has an SE of ± 1, and those numbers are added together (or subtracted), the resulting sum (or difference) has an SE of A useful rule to remember is that the SE of the sum or difference of two equally precise numbers is about 40 percent larger than the SE of one of the numbers. When two numbers of different precision are combined (added or subtracted), the precision of the result is determined mainly by the less precise number (the one with the larger SE). If one number has an SE of ± 1 and another has an SE of ± 5, the SE of the sum or difference of these two nu
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Error Propagation Excel
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Average Deviation (d) Conflicts (e) Standard Error in the Mean 3. What does uncertainty tell me? Range of possible values 4. Relative and Absolute error 5. Propagation of errors (a) add/subtract (b) multiply/divide (c) powers (d) mixtures of +-*/ (e) other http://users.auth.gr/~gasim/ErrorAnalysis/Uncertaintiespart2.html functions 6. Rounding answers properly 7. Significant figures 8. Problems to try 9. Glossary of https://www.youtube.com/watch?v=1Ip4L0193LI terms (all terms that are bold face and underlined) Part II Graphing Part III The Vernier Caliper In this manual there will be problems for you to try. They are highlighted in yellow, and have answers. There are also examples highlighted in green. 1. Systematic and random errors. 2. Determining random errors. 3. What is the range of possible values? 4. error propagation Relative and Absolute Errors 5. Propagation of Errors, Basic Rules Suppose two measured quantities x and y have uncertainties, Dx and Dy, determined by procedures described in previous sections: we would report (x ± Dx), and (y ± Dy). From the measured quantities a new quantity, z, is calculated from x and y. What is the uncertainty, Dz, in z? For the purposes of this course we will use a simplified version of the proper statistical treatment. propagation error subtraction The formulas for a full statistical treatment (using standard deviations) will also be given. The guiding principle in all cases is to consider the most pessimistic situation. Full explanations are covered in statistics courses. The examples included in this section also show the proper rounding of answers, which is covered in more detail in Section 6. The examples use the propagation of errors using average deviations. (a) Addition and Subtraction: z = x + y or z = x - y Derivation: We will assume that the uncertainties are arranged so as to make z as far from its true value as possible. Average deviations Dz = |Dx| + |Dy| in both cases With more than two numbers added or subtracted we continue to add the uncertainties. Using simpler average errors Using standard deviations Eq. 1a Eq. 1b Example: w = (4.52 ± 0.02) cm, x = ( 2.0 ± 0.2) cm, y = (3.0 ± 0.6) cm. Find z = x + y - w and its uncertainty. z = x + y - w = 2.0 + 3.0 - 4.5 = 0.5 cm Dz = Dx + Dy + Dw = 0.2 + 0.6 + 0.02 = 0.82 rounding to 0.8 cm So z = (0.5 ± 0.8) cm Solution with standard deviations, Eq. 1b, Dz = 0.633 cmz = (0.5 ± 0.6) cm Noti
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