Error Propagation In Measurement
Contents |
uncertainty of an answer obtained from a calculation. Every time data are measured, there is an uncertainty associated with that measurement. (Refer error propagation analysis to guide to Measurement and Uncertainty.) If these measurements used in your systematic error propagation calculation have some uncertainty associated with them, then the final answer will, of course, have some level
Error Propagation Example
of uncertainty. For instance, in lab you might measure an object's position at different times in order to find the object's average velocity. Since both distance and time
Error Propagation Division
measurements have uncertainties associated with them, those uncertainties follow the numbers throughout the calculations and eventually affect your final answer for the velocity of that object. How would you determine the uncertainty in your calculated values? In lab, graphs are often used where LoggerPro software calculates uncertainties in slope and intercept values for you. In other error propagation physics classes, like chemistry, there are particular ways to calculate uncertainties. In fact, since uncertainty calculations are based on statistics, there are as many different ways to determine uncertainties as there are statistical methods. The error propagation methods presented in this guide are a set of general rules that will be consistently used for all levels of physics classes in this department. In the following examples: q is the result of a mathematical operation δ is the uncertainty associated with a measurement. For example, if you have a measurement that looks like this: m = 20.4 kg ±0.2 kg Thenq = 20.4 kg and δm = 0.2 kg First Step: Make sure that your units are consistent Make sure that you are using SI units and that they are consistent. If you are converting between unit systems, then you are probably multiplying your value by a constant. Please see the following rule on how to use constants. Logger Pro If you are using a curve fit generated by Logger
uncertainty of an answer obtained from a calculation. Every time data are measured, there is an uncertainty associated with that measurement. (Refer
Error Propagation Calculus
to guide to Measurement and Uncertainty.) If these measurements used in error propagation khan academy your calculation have some uncertainty associated with them, then the final answer will, of course, have some error propagation average level of uncertainty. For instance, in lab you might measure an object's position at different times in order to find the object's average velocity. Since both distance http://physics.appstate.edu/undergraduate-programs/laboratory/resources/error-propagation and time measurements have uncertainties associated with them, those uncertainties follow the numbers throughout the calculations and eventually affect your final answer for the velocity of that object. How would you determine the uncertainty in your calculated values? In lab, graphs are often used where LoggerPro software calculates uncertainties in slope and intercept values for you. http://physics.appstate.edu/undergraduate-programs/laboratory/resources/error-propagation In other classes, like chemistry, there are particular ways to calculate uncertainties. In fact, since uncertainty calculations are based on statistics, there are as many different ways to determine uncertainties as there are statistical methods. The error propagation methods presented in this guide are a set of general rules that will be consistently used for all levels of physics classes in this department. In the following examples: q is the result of a mathematical operation δ is the uncertainty associated with a measurement. For example, if you have a measurement that looks like this: m = 20.4 kg ±0.2 kg Thenq = 20.4 kg and δm = 0.2 kg First Step: Make sure that your units are consistent Make sure that you are using SI units and that they are consistent. If you are converting between unit systems, then you are probably multiplying your value by a constant. Please see the following rule on how to use constants. Logger Pro If you are using a cu
The approach to uncertainty analysis that has been followed up to this point in the discussion has been what is called a top-down approach. Uncertainty components are estimated from direct repetitions of the measurement result. To contrast this with a propagation of error approach, consider http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm the simple example where we estimate the area of a rectangle from replicate measurements of https://www.youtube.com/watch?v=V0ZRvvHfF0E length and width. The area $$ area = length \cdot width $$ can be computed from each replicate. The standard deviation of the reported area is estimated directly from the replicates of area. Advantages of top-down approach This approach has the following advantages: proper treatment of covariances between measurements of length and width proper treatment of unsuspected sources error propagation of error that would emerge if measurements covered a range of operating conditions and a sufficiently long time period independence from propagation of error model Propagation of error approach combines estimates from individual auxiliary measurements The formal propagation of error approach is to compute: standard deviation from the length measurements standard deviation from the width measurements and combine the two into a standard deviation for area using the approximation for products of error propagation in two variables (ignoring a possible covariance between length and width), $$ s_{area} = \sqrt{width^2 \cdot s_{length}^2 + length^2 \cdot s_{width}^2} $$ Exact formula Goodman (1960) derived an exact formula for the variance between two products. Given two random variables, \(x\) and \(y\) (correspond to width and length in the above approximate formula), the exact formula for the variance is: $$ V(\bar{x} \bar{y}) = \frac{1}{n} \left[ X^2 V(y) + Y^2 V(x) + 2XYE_{11} + 2X\frac{E_{12}}{n} + 2Y\frac{E_{21}}{n} + \frac{V(x) V(y)}{n} + \frac{Cov((\Delta x)^2, (\Delta y)^2) -E_{11}^2 }{n^2} \right] $$ with \(X = E(x)\) and \(Y = E(y)\) (corresponds to width and length, respectively, in the approximate formula) \(V(x)\) is the variance of \(x\) and \(V(y)\) is the variance \(y\) (corresponds to \(s^2\) for width and length, respectively, in the approximate formula) \( E_{ij} = {(\Delta x)^i, (\Delta y)^j}\) where \( \Delta x = x - X \) and \( \Delta y = y - Y \) \( Cov((\Delta x)^2, (\Delta y)^2) = E_{22} - V(x) V(y) \) To obtain the standard deviation, simply take the square root of the above formula. Also, an estimate of the statistic is obtained by substituting sample estimates for the corresponding population values on the right hand side of the equation. Approximate formula assumes indpendence The approximate formula ass
auf Deutsch. Du kannst diese Einstellung unten ändern. Learn more You're viewing YouTube in German. You can change this preference below. Schließen Ja, ich möchte sie behalten Rückgängig machen Schließen Dieses Video ist nicht verfügbar. WiedergabelisteWarteschlangeWiedergabelisteWarteschlange Alle entfernenBeenden Wird geladen... Wiedergabeliste Warteschlange __count__/__total__ Propagation of Errors paulcolor AbonnierenAbonniertAbo beenden6060 Wird geladen... Wird geladen... Wird verarbeitet... Hinzufügen Möchtest du dieses Video später noch einmal ansehen? Wenn du bei YouTube angemeldet bist, kannst du dieses Video zu einer Playlist hinzufügen. Anmelden Teilen Mehr Melden Möchtest du dieses Video melden? Melde dich an, um unangemessene Inhalte zu melden. Anmelden Transkript Statistik 29.819 Aufrufe 229 Dieses Video gefällt dir? Melde dich bei YouTube an, damit dein Feedback gezählt wird. Anmelden 230 7 Dieses Video gefällt dir nicht? Melde dich bei YouTube an, damit dein Feedback gezählt wird. Anmelden 8 Wird geladen... Wird geladen... Transkript Das interaktive Transkript konnte nicht geladen werden. Wird geladen... Wird geladen... Die Bewertungsfunktion ist nach Ausleihen des Videos verfügbar. Diese Funktion ist zurzeit nicht verfügbar. Bitte versuche es später erneut. Veröffentlicht am 13.11.2013Educational video: How to propagate the uncertainties on measurements in the physics lab Kategorie Bildung Lizenz Standard-YouTube-Lizenz Mehr anzeigen Weniger anzeigen Wird geladen... Autoplay Wenn Autoplay aktiviert ist, wird die Wiedergabe automatisch mit einem der aktuellen Videovorschläge fortgesetzt. Nächstes Video Propagation of Error - Dauer: 7:01 Matt Becker 10.709 Aufrufe 7:01 Propagation of Uncertainty, Parts 1 and 2 - Dauer: 16:31 Robbie Berg 21.912 Aufrufe 16:31 AP/IB Physics 0-3 - Propagation of Error - Dauer: 12:08 msquaredphysics 70 Aufrufe 12:08 Basic Rules of Multiplication,Division and Exponent of Errors(Part-2), IIT-JEE physics classes - Dauer: 8:52 IIT-JEE Physics Classes 765 Aufrufe 8:52 IB Physics- Uncertainty and Error Propagation - Dauer: 7:05 Gilberto Santos 1.043 Aufrufe 7:05 Measurements, Uncertainties, and Error Propagation - Dauer: 1:36:37 PhysicsOnTheBrain 44.984 Aufrufe 1:36:37 IB Physics: Uncertainties and Errors - Dauer: 18:37 Brian Lamore 47.440 Aufrufe 18:37 XI_7.Errors in measurement(2013).mp4t - Dauer: 1:49:43 Pradeep Kshetrapal 32.386 Aufrufe 1:49:43 Excel Uncertainty Calculation Video Part 1 - Dauer: 5:48 Measurements Lab 21.845 Aufrufe 5:48 Uncertainty & Measurements - Dauer: 3:01 TruckeeAPChemistry 19.103 Aufrufe 3:01 Error Propagation - Da