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This 17 page Class Notes was uploaded by Kayley Corwin on Saturday September 19, 2015. The Class Notes belongs to PHYS 3110 at University of Houston taught by Rebecca Forrest in Fall. Since its upload, it has received 46 views. For similar materials see /class/208343/phys-3110-university-of-houston in Physics 2 at University of Houston.
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Date Created: 09/19/15
Error Analysis PHYS 3110 Types of Error Instrumental Observational Environmental Theoretical Types of Error Instrumental Accuracy limits of instrument Poorly calibrated instrument Broken instrument Observational Environmental Theoretical Types of Error Instrumental Observational Parallax Misused instrument Environmental Theoretical Types of Error Instrumental Observational Environmental Electrical power brownout causing low current Local magnetic field not accounted for wind Theoretical Types of Error Instrumental Observational Environmental Theoretical Effects not accounted for or incorrectly ignored Friction Error in equations Types of Error Random n r Can be quantified by statistical l analysis True Value Systematic H I Try to identify and get rid of l Hopefully found during True Value analysis may need to repeat experiment Statistical Analysis of Random Error For n measurements they should group around the true value For large n the average should tend to the true value lfthe measurements are independent can find the standard deviation 0 o is the width of the distribution 37 x 1 n 372 in quoti1 Standard deviation of the mean omon 2 1 n 2 Gm X X i1 For n gt 1 measured values report X 7i om If om 0 use accuracy of measurement device for reported error If there is no systematic error there is a 23 probability that the true value is within ism Reporting Error Yicm Significant figures cm one sometimes two sig figs xave same accuracy as cm 6 1602176 5 X1039190000 OOO1X1O3919 C G and Gm 0 represents the error in one measurement cm represents the error in the mean of n measurements Gaussian Distribution Plot of measured value versus number N of times that value was measured IF error is random for large n this distribution tends to a 6 Gaussian distribution 24 PX NXn X 2 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 NX m6 9 26 thm 26 Gaussian Distribution The probability of a measurement being within YG 6 Ofxave39 Pwithin0 jPxdx Probability of being within 15 683 2c 955 35 997 Poisson Distribution X i X e 00 W 2 2882 Applies to processes a 004 003 described by an 002 001 exponential such as 0 radioactive decay 0 5 10 15 20 25 30 35 6 X Xave For large xave ie for long Gaussian 1 G 120 counting times the 447 Poisson distribution tends Gaussian 2 G 6 to the Gaussian distribution Reporting Error from a Poisson Process When measuring a physical process that you expect to follow a Poisson distribution the error in one measurement is xXioXiVX Example Measuring the intensity of radiation emitted by an or source and scattered by gold nuclei at an angle 9 over 30 seconds Propagation of Errors Determining the error in a quantity calculated from measured data Let x y 2 be measured values Let 8x 8y 82 be the corresponding estimated errors in the measurements x 1 8x etc If one measurement 8x precision of the instrument If n measurements of x then use x oX where ox is the standard deviation of the mean of x
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