Propagation Of Random Error
Contents |
propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements error propagation rules they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate to
Error Propagation Calculator
the combination of variables in the function. The uncertainty u can be expressed in a number of ways. It may
Error Propagation Physics
be defined by the absolute error Δx. Uncertainties can also be defined by the relative error (Δx)/x, which is usually written as a percentage. Most commonly, the uncertainty on a quantity is
Error Propagation Chemistry
quantified in terms of the standard deviation, σ, the positive square root of variance, σ2. The value of a quantity and its error are then expressed as an interval x ± u. If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe the region within which the true value of the error propagation square root variable may be found. For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are ± one standard deviation from the value, that is, there is approximately a 68% probability that the true value lies in the region x ± σ. If the uncertainties are correlated then covariance must be taken into account. Correlation can arise from two different sources. First, the measurement errors may be correlated. Second, when the underlying values are correlated across a population, the uncertainties in the group averages will be correlated.[1] Contents 1 Linear combinations 2 Non-linear combinations 2.1 Simplification 2.2 Example 2.3 Caveats and warnings 2.3.1 Reciprocal 2.3.2 Shifted reciprocal 3 Example formulas 4 Example calculations 4.1 Inverse tangent function 4.2 Resistance measurement 5 See also 6 References 7 Further reading 8 External links Linear combinations[edit] Let { f k ( x 1 , x 2 , … , x n ) } {\displaystyle \ ≈ 7(x_ ≈ 6,x_ ≈ 5,\dots ,x_ ≈ 4)\}} be a set of m functions which are linear combinations of n {\displaystyle n} variables x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},
Επιλέξτε τη γλώσσα propagated error calculus σας. Κλείσιμο Μάθετε περισσότερα View https://en.wikipedia.org/wiki/Propagation_of_uncertainty this message in English Το YouTube εμφανίζεται στα Ελληνικά. Μπορείτε να https://www.youtube.com/watch?v=V0ZRvvHfF0E αλλάξετε αυτή την προτίμηση παρακάτω. Learn more You're viewing YouTube in Greek. You can change this preference below. Κλείσιμο Ναι, θέλω να τη κρατήσω Αναίρεση Κλείσιμο Αυτό το βίντεο δεν είναι διαθέσιμο.
or more quantities, each with their individual uncertainties, and then combine the information from these quantities in order to come up with a final result of our experiment. How can you state your answer for the combined result of these measurements and http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm their uncertainties scientifically? The answer to this fairly common question depends on how the individual measurements are combined in the result. We will treat each case separately: Addition of measured quantities If you have measured values for the quantities X, Y, and Z, with uncertainties dX, dY, and dZ, and your final result, R, is the sum or difference of these quantities, then the uncertainty dR is: Here the upper equation error propagation is an approximation that can also serve as an upper bound for the error. Please note that the rule is the same for addition and subtraction of quantities. Example: Suppose we have measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. Then the displacement is: Dx = x2-x1 = 14.4 m - 9.3 m = 5.1 m and the error in the displacement is: propagation of random (0.22 + 0.32)1/2 m = 0.36 m Multiplication of measured quantities In the same way as for sums and differences, we can also state the result for the case of multiplication and division: Again the upper line is an approximation and the lower line is the exact result for independent random uncertainties in the individual variables. And again please note that for the purpose of error calculation there is no difference between multiplication and division. Example: We have measured a displacement of x = 5.1+-0.4 m during a time of t = 0.4+-0.1 s. What is the average velocity and the error in the average velocity? v = x / t = 5.1 m / 0.4 s = 12.75 m/s and the uncertainty in the velocity is: dv = |v| [ (dx/x)2 + (dt/t)2 ]1/2 = 12.75 m/s [(0.4/5.1)2 + (0.1/0.4)2]1/2 = 3.34 m/s Multiplication with a constant What if you have measured the uncertainty in an observable X, and you need to multiply it with a constant that is known exactly? What is the error then? This is easy: just multiply the error in X with the absolute value of the constant, and this will give you the error in R: If you compare this to the above rule for multiplication of t
be down. Please try the request again. Your cache administrator is webmaster. Generated Mon, 24 Oct 2016 17:21:59 GMT by s_wx1085 (squid/3.5.20)