Modern Methods of Data Analysis - WS 07/08
|
|
- Mary Mitchell
- 5 years ago
- Views:
Transcription
1 Modern Methods of Data Analysis Lecture VIa ( ) Contents: Uncertainties (II): Re: error propagation Correlated uncertainties Systematic uncertainties
2 Re: Error Propagation (I) x = Vi,j and µi known y(x) is function of first order Taylor expansion...
3 Re: Error Propagation (II)
4 Re: Gaussian error propagation Error estimates for functions of several correlated variables : Additional terms accounting Normal errors for correlations for uncorrelated variables Special case, uncorrelated variables: This is called Gaussian error propagation, however has nothing to do with Gaussian distributions Modern Methods of Data Analysis - WS 07/08
5 And the same in more dimensions (A is Jacobi matrix)
6 Be aware... The approximation using Taylor expansion breaks down if the function is significantly not linear in the region ± 1σ around the mean value. Example: momentum estimate in B field; p ~ 1/κ 10 % momentum bias!
7 2. Order Taylor Expansion
8 Example Systematic Error Measurements are taken with a steel ruler, the ruler was calibrated at 15C, but the measurements were carried out at 22C. This is a systematic mistake (bias) and not a systematic uncertainty! To neglect this effect is a systematic mistake. Effects can be corrected for! If the temperature coefficient and lab temperature is known (exactly), then there is no systematic uncertainty. If we correct for effect, but corrections are not known exactly, then we have to introduce a systematic uncertainty. In practice (unfortunately): often not corrected for such effects, but then just included in sys. errors.
9 Systematic Error Definition: A systematic error denotes the uncertainty in effects caused by systematic mistakes and caused by neglecting systematic mistakes A systematic mistake is not a systematic error. Comments on systematic errors: sys. error do NOT decrease with 1/ N statistical and systematic errors can in general be added in quadrature (if uncorrelated; else include correlations) need to quote them separately in the results, they are often correlated among experiments: m(b0) = ± 0.53 (stat) ± 0.33 (sys)
10 Combing Errors (I) Suppose you have two measurements, with a random (statistical) uncertainties and a common systematic error S. How to make the covariance matrix?
11 Combining Errors (II) Consider and as sum of three random variables: assign according uncertainties More extended case, three measurements with one common systematic uncertainty S, and one systematic uncertainty T common for two of the measurements
12 Example: Pendulum Measure length of bar by measuring period of pendelum. Take two time measurements at different temperature. Compute the difference in length: and associated uncertainties. Given statistical uncertainties on the time measurements, additional common systematic uncertainty on the time measurement ( )and common systematic uncertainty on g ( ).
13 Evaluating Systematic Errors (I) Distinguish systematic errors from known and from unsuspected sources known sources error on factors in the analysis, energy calibration, tracking efficiencies, corrections,... error on external input: theory error, error on branching ratios, masses, fragmentation evaluate systematic uncertainties from known sources s(i) on result R. take several typical assumptions on s(i), compute R for each of them. Compute standard deviation of R take two extreme assumptions, compute R. Take difference of results divided by 12
14 Evaluating Systematic Errors (II) Errors from unsuspected sources need first to be identified repeat the analysis in different form helps to find systematic effects vary the range of data used for extraction of the result, use subset of data change cuts, change histogram binning change parameterizations, change fit techniques look for impossibilities It is clearly wrong to add in quadrature resulting deviations from the check list as systematic error this is misconception Moreover, the more careful you are doing more checks, the bigger should your systematic be??? - No! Modern Methods of Data Analysis - WS 07/08
15 Evaluating Systematic Errors (III) define before the consistency checks a pass/fail criteria. Remember with 20 checks you expect on average one 2σ deviation. However uncertainties are highly correlated! if you do not expect a systematic effect a priori and if the deviation is not significant, then do not add this in the systematic error if there is a deviation, try to understand, where the mistake is in the analysis and fix it! only as a last resort include discrepancy in systematic error
16 Evaluating Systematic Errors (IV) Conservative estimate of uncertainties.. Physicists tend to overestimate their systematics: If we estimate them conservatively, we are save in case we have forgotten to evaluate one source. How can we be sure that this identified source is covered by the conservative uncertainties??!! This is (commonly used) non-sense.
Modern Methods of Data Analysis - WS 07/08
Modern Methods of Data Analysis Lecture V (12.11.07) Contents: Central Limit Theorem Uncertainties: concepts, propagation and properties Central Limit Theorem Consider the sum X of n independent variables,
More informationPhysics 1140 Fall 2013 Introduction to Experimental Physics
Physics 1140 Fall 2013 Introduction to Experimental Physics Joanna Atkin Lecture 5: Recap of Error Propagation and Gaussian Statistics Graphs and linear fitting Experimental analysis Typically make repeat
More informationPHYSICS 2150 LABORATORY
PHYSICS 2150 LABORATORY Instructors: John Cumalat Jiayan Pheonix Dai Lab Coordinator: Jerry Leigh Lecture 2 September 2, 2008 PHYS2150 Lecture 2 Need to complete the Radiation Certification The Gaussian
More informationUncertainty and Bias UIUC, 403 Advanced Physics Laboratory, Fall 2014
Uncertainty and Bias UIUC, 403 Advanced Physics Laboratory, Fall 2014 Liang Yang* There are three kinds of lies: lies, damned lies and statistics. Benjamin Disraeli If your experiment needs statistics,
More informationStatistics. Lent Term 2015 Prof. Mark Thomson. 2: The Gaussian Limit
Statistics Lent Term 2015 Prof. Mark Thomson Lecture 2 : The Gaussian Limit Prof. M.A. Thomson Lent Term 2015 29 Lecture Lecture Lecture Lecture 1: Back to basics Introduction, Probability distribution
More informationPHYSICS 2150 LABORATORY
PHYSICS 2150 LABORATORY Instructors: Noel Clark James G. Smith Eric D. Zimmerman Lab Coordinator: Jerry Leigh Lecture 2 January 22, 2008 PHYS2150 Lecture 2 Announcements/comments The Gaussian distribution
More informationMeasurements of a Table
Measurements of a Table OBJECTIVES to practice the concepts of significant figures, the mean value, the standard deviation of the mean and the normal distribution by making multiple measurements of length
More informationPHY 123 Lab 1 - Error and Uncertainty and the Simple Pendulum
To print higher-resolution math symbols, click the Hi-Res Fonts for Printing button on the jsmath control panel. PHY 13 Lab 1 - Error and Uncertainty and the Simple Pendulum Important: You need to print
More informationData and Error analysis
Data and Error analysis Wednesday, January 15, 2014 3:07 PM References: 1. [EMP] Experiments in modern physics, Ch. 10 2. [Lyons] Practical guide to data analysis for physical science students, by Louis
More informationNormal Distributions Rejection of Data + RLC Circuits. Lecture 4 Physics 2CL Summer 2011
Normal Distributions Rejection of Data + RLC Circuits Lecture 4 Physics 2CL Summer 2011 Outline Reminder of simple uncertainty propagation formulae Hidden useful formula for estimating uncertainties More
More informationErrors: What they are, and how to deal with them
Errors: What they are, and how to deal with them A series of three lectures plus exercises, by Alan Usher Room 111, a.usher@ex.ac.uk Synopsis 1) Introduction ) Rules for quoting errors 3) Combining errors
More informationPhysics 509: Error Propagation, and the Meaning of Error Bars. Scott Oser Lecture #10
Physics 509: Error Propagation, and the Meaning of Error Bars Scott Oser Lecture #10 1 What is an error bar? Someone hands you a plot like this. What do the error bars indicate? Answer: you can never be
More informationMeasurement and Uncertainty
Measurement and Uncertainty Michael Gold Physics 307L September 16, 2006 Michael Gold (Physics 307L) Measurement and Uncertainty September 16, 2006 1 / 9 Goal of Experiment Measure a parameter: statistical
More informationLAB INFORMATION TFYA76 Mekanik
LAB INFORMATION TFYA76 Mekanik September 18, 2018 Lecturer: Bo Durbeej (bo.durbeej@liu.se) Lab Assistants: Tim Cornelissen (tim.cornelissen@liu.se) Indre Urbanaviciute (indre.urbanaviciute@liu.se) Contents
More informationPhysics 509: Propagating Systematic Uncertainties. Scott Oser Lecture #12
Physics 509: Propagating Systematic Uncertainties Scott Oser Lecture #1 1 Additive offset model Suppose we take N measurements from a distribution, and wish to estimate the true mean of the underlying
More informationAveraging, Errors and Uncertainty
Averaging, Errors and Uncertainty Types of Error There are three types of limitations to measurements: 1) Instrumental limitations Any measuring device can only be used to measure to with a certain degree
More informationPhysics 403. Segev BenZvi. Propagation of Uncertainties. Department of Physics and Astronomy University of Rochester
Physics 403 Propagation of Uncertainties Segev BenZvi Department of Physics and Astronomy University of Rochester Table of Contents 1 Maximum Likelihood and Minimum Least Squares Uncertainty Intervals
More informationLecture 2: Reporting, Using, and Calculating Uncertainties 2. v = 6050 ± 30 m/s. v = 6047 ± 3 m/s
1 CHAPTER 2: Reporting and Using Uncertainties Quoting a result as: Best Estimate ± Uncertainty In the Archimedes experiment result, we had a table which read Measurement of Crown Density by Two Experts
More informationBRIDGE CIRCUITS EXPERIMENT 5: DC AND AC BRIDGE CIRCUITS 10/2/13
EXPERIMENT 5: DC AND AC BRIDGE CIRCUITS 0//3 This experiment demonstrates the use of the Wheatstone Bridge for precise resistance measurements and the use of error propagation to determine the uncertainty
More informationError analysis for IPhO contestants
Error analysis for IPhO contestants Heikki Mäntysaari University of Jyväskylä, Department of Physics Abstract In the experimental part of IPhO (and generally when performing measurements) you have to estimate
More informationPHYSICS 2150 EXPERIMENTAL MODERN PHYSICS. Lecture 3 Rejection of Data; Weighted Averages
PHYSICS 15 EXPERIMENTAL MODERN PHYSICS Lecture 3 Rejection of Data; Weighted Averages PREVIOUS LECTURE: GAUSS DISTRIBUTION 1.5 p(x µ, )= 1 e 1 ( x µ ) µ=, σ=.5 1. µ=3, σ=.5.5 µ=4, σ=1 4 6 8 WE CAN NOW
More informationLab 1: Measurement, Uncertainty, and Uncertainty Propagation
Lab 1: Measurement, Uncertainty, and Uncertainty Propagation 17 ame Date Partners TA Section Lab 1: Measurement, Uncertainty, and Uncertainty Propagation The first principle is that you must not fool yourself
More informationUncertainty, Measurement, and Models Overview Exp #1. Lecture # 2 Physics 2BL Summer Session I 2015
Uncertainty, Measurement, and Models Overview Exp #1 Lecture # 2 Physics 2BL Summer Session I 2015 Outline What uncertainty (error) analysis can for you Issues with measurement and observation What does
More informationStatistics and Data Analysis
Statistics and Data Analysis The Crash Course Physics 226, Fall 2013 "There are three kinds of lies: lies, damned lies, and statistics. Mark Twain, allegedly after Benjamin Disraeli Statistics and Data
More informationData and Error Analysis
Data and Error Analysis Introduction In this lab you will learn a bit about taking data and error analysis. The physics of the experiment itself is not the essential point. (Indeed, we have not completed
More informationProbability & Statistics: Introduction. Robert Leishman Mark Colton ME 363 Spring 2011
Probability & Statistics: Introduction Robert Leishman Mark Colton ME 363 Spring 2011 Why do we care? Why do we care about probability and statistics in an instrumentation class? Example Measure the strength
More informationSTATISTICS OF OBSERVATIONS & SAMPLING THEORY. Parent Distributions
ASTR 511/O Connell Lec 6 1 STATISTICS OF OBSERVATIONS & SAMPLING THEORY References: Bevington Data Reduction & Error Analysis for the Physical Sciences LLM: Appendix B Warning: the introductory literature
More informationAppendix C: Accuracy, Precision, and Uncertainty
Appendix C: Accuracy, Precision, and Uncertainty How tall are you? How old are you? When you answered these everyday questions, you probably did it in round numbers such as "five foot, six inches" or "nineteen
More informationCourse Project. Physics I with Lab
COURSE OBJECTIVES 1. Explain the fundamental laws of physics in both written and equation form 2. Describe the principles of motion, force, and energy 3. Predict the motion and behavior of objects based
More informationIntermediate Lab PHYS 3870
Intermediate Lab PHYS 3870 Lecture 4 Comparing Data and Models Quantitatively Linear Regression Introduction Section 0 Lecture 1 Slide 1 References: Taylor Ch. 8 and 9 Also refer to Glossary of Important
More informationElectromagnetism lab project
Electromagnetism lab project Contents 1. Overview of the course 2. How to analyse errors in measurements 3. How to make graphical representations (plots) Overview Four lab experiments Biot Savart s law
More informationUncertainty, Error, and Precision in Quantitative Measurements an Introduction 4.4 cm Experimental error
Uncertainty, Error, and Precision in Quantitative Measurements an Introduction Much of the work in any chemistry laboratory involves the measurement of numerical quantities. A quantitative measurement
More information1 Measurement Uncertainties
1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.
More informationStatistical Methods in Particle Physics
Statistical Methods in Particle Physics Lecture 10 December 17, 01 Silvia Masciocchi, GSI Darmstadt Winter Semester 01 / 13 Method of least squares The method of least squares is a standard approach to
More informationPHYS 352. On Measurement, Systematic and Statistical Errors. Errors in Measurement
PHYS 352 On Measurement, Systematic and Statistical Errors Errors in Measurement when you make a measurement you should quote an estimate of the uncertainty or error all measurements have systematic errors
More informationExperiment 2: Projectile motion and conservation of energy
Experiment 2: Projectile motion and conservation of energy Nate Saffold nas2173@columbia.edu Office Hour: Mondays, 5:30PM-6:30PM @ Pupin 1216 INTRO TO EXPERIMENTAL PHYS-LAB 1494/2699 Overview The physics
More informationMeasurements and Data Analysis
Measurements and Data Analysis 1 Introduction The central point in experimental physical science is the measurement of physical quantities. Experience has shown that all measurements, no matter how carefully
More informationError analysis for the physical sciences A course reader for phys 1140 Scott Pinegar and Markus Raschke Department of Physics, University of Colorado
Error analysis for the physical sciences A course reader for phys 1140 Scott Pinegar and Markus Raschke Department of Physics, University of Colorado Version 1.0 (September 9, 2012) 1 Part 1 (chapter 1
More informationThe SuperBall Lab. Objective. Instructions
1 The SuperBall Lab Objective This goal of this tutorial lab is to introduce data analysis techniques by examining energy loss in super ball collisions. Instructions This laboratory does not have to be
More informationLecture 10. Lidar Simulation and Error Analysis Overview (2)
Lecture 10. Lidar Simulation and Error Analysis Overview () Introduction Accuracy versus Precision Classification of Measurement Errors Accuracy in lidar measurements Precision in lidar measurements General
More informationAppendix B: Accuracy, Precision and Uncertainty
Appendix B: Accuracy, Precision and Uncertainty How tall are you? How old are you? When you answered these everyday questions, you probably did it in round numbers such as "five foot, six inches" or "nineteen
More informationIntroduction to the General Physics Laboratories
Introduction to the General Physics Laboratories September 5, 2007 Course Goals The goal of the IIT General Physics laboratories is for you to learn to be experimental scientists. For this reason, you
More informationEM Waves in Media. What happens when an EM wave travels through our model material?
EM Waves in Media We can model a material as made of atoms which have a charged electron bound to a nucleus by a spring. We model the nuclei as being fixed to a grid (because they are heavy, they don t
More informationPhysics 115 Experiment 1. Introduction to Measurement and Error Analysis (PHY 115 and 117)
Physics 115 Experiment 1 Introduction to Measurement and Error Analysis (PHY 115 and 117) Introduction In the sciences, measurement plays an important role. The accuracy of the measurement, as well as
More informationUniversity of Massachusetts Boston - Chemistry Department Physical Chemistry Laboratory Introduction to Maximum Probable Error
University of Massachusetts Boston - Chemistry Department Physical Chemistry Laboratory Introduction to Maximum Probable Error Statistical methods describe random or indeterminate errors in experimental
More informationError Analysis. V. Lorenz L. Yang, M. Grosse Perdekamp, D. Hertzog, R. Clegg PHYS403 Spring 2016
Error Analysis V. Lorenz L. Yang, M. Grosse Perdekamp, D. Hertzog, R. Clegg PHYS403 Spring 2016 Reporting measurement results Always include uncertainty estimates in your results Have the correct number
More informationElectricity Designing a Voltmeter c 2 testing Review. Lecture # 7 Physics 2BL Summer 2011
Electricity Designing a Voltmeter c 2 testing Review Lecture # 7 Physics 2BL Summer 2011 Announcements CAPE evaluations: Important for fine tuning of the course Making changes Giving feedback Name for
More informationInstrumentation & Measurement AAiT. Chapter 2. Measurement Error Analysis
Chapter 2 Measurement Error Analysis 2.1 The Uncertainty of Measurements Some numerical statements are exact: Mary has 3 brothers, and 2 + 2 = 4. However, all measurements have some degree of uncertainty
More informationIntroduction to Data Analysis
Introduction to Data Analysis Analysis of Experimental Errors How to Report and Use Experimental Errors Statistical Analysis of Data Simple statistics of data Plotting and displaying the data Summary Errors
More informationPhysics: Uncertainties - Student Material (AH) 1
UNCERTAINTIES Summary of the Basic Theory associated with Uncertainty It is important to realise that whenever a physical quantity is being measured there will always be a degree of inaccuracy associated
More informationModern Methods of Data Analysis - WS 07/08
Modern Methods of Data Analysis Lecture VII (26.11.07) Contents: Maximum Likelihood (II) Exercise: Quality of Estimators Assume hight of students is Gaussian distributed. You measure the size of N students.
More informationTyping Equations in MS Word 2010
CM3215 Fundamentals of Chemical Engineering Laboratory Typing Equations in MS Word 2010 https://www.youtube.com/watch?v=cenp9mehtmy Professor Faith Morrison Department of Chemical Engineering Michigan
More informationERRORS AND THE TREATMENT OF DATA
M. Longo ERRORS AND THE TREATMENT OF DATA Essentially all experimental quantities have an uncertainty associated with them. The only exceptions are a few defined quantities like the wavelength of the orange-red
More informationLecture 5. G. Cowan Lectures on Statistical Data Analysis Lecture 5 page 1
Lecture 5 1 Probability (90 min.) Definition, Bayes theorem, probability densities and their properties, catalogue of pdfs, Monte Carlo 2 Statistical tests (90 min.) general concepts, test statistics,
More informationUncertainty, Measurement, and Models. Lecture 2 Physics 2CL Summer Session 2011
Uncertainty, Measurement, and Models Lecture 2 Physics 2CL Summer Session 2011 Outline What is uncertainty (error) analysis and what can it do for you Issues with measurement and observation What does
More informationAppendix II Calculation of Uncertainties
Part 1: Sources of Uncertainties Appendix II Calculation of Uncertainties In any experiment or calculation, uncertainties can be introduced from errors in accuracy or errors in precision. A. Errors in
More informationExperiment 2. Reaction Time. Make a series of measurements of your reaction time. Use statistics to analyze your reaction time.
Experiment 2 Reaction Time 2.1 Objectives Make a series of measurements of your reaction time. Use statistics to analyze your reaction time. 2.2 Introduction The purpose of this lab is to demonstrate repeated
More information1 Measurement Uncertainties
1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.
More informationBRIEF SURVEY OF UNCERTAINITY IN PHYSICS LABS
BRIEF SURVEY OF UNCERTAINITY IN PHYSICS LABS THREE CASES OF UNCERTAINTY CALCULATION There are two main situations when dealing with uncertainty calculation of a given parameter; or it is measured or it
More informationIntroduction to 1118 Labs
Name: Partner(s): 1118 section: Desk # Date: Introduction to 1118 Labs Introductory materials are at: www.langaraphysics.com/lab.html. You may find following 3 links useful for this lab: Measurements:
More informationConservation of Momentum
Conservation of Momentum 1 Introduction In this lab you will investigate conservation of momentum and the concepts of elastic and inelastic collisions. You will use similar techniques that you developed
More informationIntroduction to Statistics and Error Analysis
Introduction to Statistics and Error Analysis Physics116C, 4/3/06 D. Pellett References: Data Reduction and Error Analysis for the Physical Sciences by Bevington and Robinson Particle Data Group notes
More informationAdvanced Statistical Methods. Lecture 6
Advanced Statistical Methods Lecture 6 Convergence distribution of M.-H. MCMC We denote the PDF estimated by the MCMC as. It has the property Convergence distribution After some time, the distribution
More informationEXPERIMENT: REACTION TIME
EXPERIMENT: REACTION TIME OBJECTIVES to make a series of measurements of your reaction time to make a histogram, or distribution curve, of your measured reaction times to calculate the "average" or "mean"
More informationStatistical Methods in Particle Physics Lecture 1: Bayesian methods
Statistical Methods in Particle Physics Lecture 1: Bayesian methods SUSSP65 St Andrews 16 29 August 2009 Glen Cowan Physics Department Royal Holloway, University of London g.cowan@rhul.ac.uk www.pp.rhul.ac.uk/~cowan
More informationPHYS 2211L - Principles of Physics Laboratory I Propagation of Errors Supplement
PHYS 2211L - Principles of Physics Laboratory I Propagation of Errors Supplement 1. Introduction. Whenever two or more quantities are measured directly in order to indirectly determine the value of another,
More informationName: Section #: Date: The Pendulum
ASU University Physics Labs - Mechanics Lab 9 p. 1 Name: Section #: Date: Part 1 The Pendulum For Part 1 of the experiment, make a sketch of the graph you think will be produced by the simple pendulum
More informationTake the measurement of a person's height as an example. Assuming that her height has been determined to be 5' 8", how accurate is our result?
Error Analysis Introduction The knowledge we have of the physical world is obtained by doing experiments and making measurements. It is important to understand how to express such data and how to analyze
More informationPHY 101L - Experiments in Mechanics
PHY 101L - Experiments in Mechanics introduction to error analysis What is Error? In everyday usage, the word error usually refers to a mistake of some kind. However, within the laboratory, error takes
More informationLab 0 Appendix C L0-1 APPENDIX C ACCURACY OF MEASUREMENTS AND TREATMENT OF EXPERIMENTAL UNCERTAINTY
Lab 0 Appendix C L0-1 APPENDIX C ACCURACY OF MEASUREMENTS AND TREATMENT OF EXPERIMENTAL UNCERTAINTY A measurement whose accuracy is unknown has no use whatever. It is therefore necessary to know how to
More informationMEASUREMENTS AND ERRORS (OR EXPERIMENTAL UNCERTAINTIES)
MEASUREMENTS AND ERRORS (OR EXPERIMENTAL UNCERTAINTIES) Determination of Uncertainties in Measured Quantities Physics is not only a theoretical but an experimental science; it depends on measured values
More informationBRIEF SURVEY OF UNCERTAINITY IN PHYSICS LABS
BRIEF SURVEY OF UNCERTAINITY IN PHYSICS LABS THREE CASES OF UNCERTAINTY CALCULATION There are two main situations when dealing with uncertainty calculation of a given parameter; or it is measured or it
More informationIntroduction to Measurement
Units and Measurement Introduction to Measurement One of the most important steps in applying the scientific method is experiment: testing the prediction of a hypothesis. Typically we measure simple quantities
More informationExperiment 1 Simple Measurements and Error Estimation
Experiment 1 Simple Measurements and Error Estimation Reading and problems (1 point for each problem): Read Taylor sections 3.6-3.10 Do problems 3.18, 3.22, 3.23, 3.28 Experiment 1 Goals 1. To perform
More informationCalifornia State Science Fair
California State Science Fair How to Estimate the Experimental Uncertainty in Your Science Fair Project Part 2 -- The Gaussian Distribution: What the Heck is it Good For Anyway? Edward Ruth drruth6617@aol.com
More informationPhysics 1140 Lecture 6: Gaussian Distributions
Physics 1140 Lecture 6: Gaussian Distributions February 21/22, 2008 Homework #3 due Monday, 5 PM Should have taken data for Lab 3 this week - due Tues. Mar. 4, 5:30 PM Final (end of lectures) is next week
More informationExperiment 2 Random Error and Basic Statistics
PHY191 Experiment 2: Random Error and Basic Statistics 7/12/2011 Page 1 Experiment 2 Random Error and Basic Statistics Homework 2: turn in the second week of the experiment. This is a difficult homework
More information5 Error Propagation We start from eq , which shows the explicit dependence of g on the measured variables t and h. Thus.
5 Error Propagation We start from eq..4., which shows the explicit dependence of g on the measured variables t and h. Thus g(t,h) = h/t eq..5. The simplest way to get the error in g from the error in t
More informationIntroduction to Measurements & Error Analysis
Introduction to Measurements & Error Analysis The Uncertainty of Measurements Some numerical statements are exact: Mary has 3 brothers, and 2 + 2 = 4. However, all measurements have some degree of uncertainty
More informationUncertainties in AH Physics
Advanced Higher Physics Contents This booklet is one of a number that have been written to support investigative work in Higher and Advanced Higher Physics. It develops the skills associated with handling
More informationProbability Density Functions
Statistical Methods in Particle Physics / WS 13 Lecture II Probability Density Functions Niklaus Berger Physics Institute, University of Heidelberg Recap of Lecture I: Kolmogorov Axioms Ingredients: Set
More informationIntroduction to Experiment: Part 1
Introduction to Experiment: Part 1 Nate Saffold nas2173@columbia.edu Office Hours: Mondays 5-6PM Pupin 1216 INTRO TO EXPERIMENTAL PHYS-LAB 1493/1494/2699 General Announcements Labs will commence February
More informationMore Probability and Error Analysis
02/01/07 PHY310: Statistical Data Analysis 1 PHY310: Lecture 04 More Probability and Error Analysis Road Map Probability (continued) Types of Uncertainty Propagating Uncertainty Bayes Theorem with P.D.F.s
More informationMeasurement: The Basics
I. Introduction Measurement: The Basics Physics is first and foremost an experimental science, meaning that its accumulated body of knowledge is due to the meticulous experiments performed by teams of
More informationIntroduction to Statistical Methods for High Energy Physics
Introduction to Statistical Methods for High Energy Physics 2011 CERN Summer Student Lectures Glen Cowan Physics Department Royal Holloway, University of London g.cowan@rhul.ac.uk www.pp.rhul.ac.uk/~cowan
More informationModern Navigation. Thomas Herring
12.215 Modern Navigation Thomas Herring Basic Statistics Summary of last class Statistical description and parameters Probability distributions Descriptions: expectations, variances, moments Covariances
More informationStatistical Methods in Particle Physics
Statistical Methods in Particle Physics Lecture 11 January 7, 2013 Silvia Masciocchi, GSI Darmstadt s.masciocchi@gsi.de Winter Semester 2012 / 13 Outline How to communicate the statistical uncertainty
More informationError Analysis How Do We Deal With Uncertainty In Science.
How Do We Deal With Uncertainty In Science. 1 Error Analysis - the study and evaluation of uncertainty in measurement. 2 The word error does not mean mistake or blunder in science. 3 Experience shows no
More informationLab 1: Measurement and Uncertainty
3 Lab 1: Measurement and Uncertainty I. Before you come to lab... A. Read through the handout on the course website, Chapters 1-2 from Taylor, An Introduction to Error Analysis. These chapters will introduce
More informationSPH3U UNIVERSITY PHYSICS
SPH3U UNIVERSITY PHYSICS REVIEW: MATH SKILLS L (P.651; 653) Many people believe that all measurements are reliable (consistent over many trials), precise (to as many decimal places as possible), and accurate
More information26, 24, 26, 28, 23, 23, 25, 24, 26, 25
The ormal Distribution Introduction Chapter 5 in the text constitutes the theoretical heart of the subject of error analysis. We start by envisioning a series of experimental measurements of a quantity.
More informationarxiv:hep-ex/ v1 2 Jun 2000
MPI H - V7-000 May 3, 000 Averaging Measurements with Hidden Correlations and Asymmetric Errors Michael Schmelling / MPI for Nuclear Physics Postfach 03980, D-6909 Heidelberg arxiv:hep-ex/0006004v Jun
More informationTHE COMPTON EFFECT Last Revised: January 5, 2007
B2-1 THE COMPTON EFFECT Last Revised: January 5, 2007 QUESTION TO BE INVESTIGATED: How does the energy of a scattered photon change after an interaction with an electron? INTRODUCTION: When a photon is
More informationStatistics for Data Analysis. Niklaus Berger. PSI Practical Course Physics Institute, University of Heidelberg
Statistics for Data Analysis PSI Practical Course 2014 Niklaus Berger Physics Institute, University of Heidelberg Overview You are going to perform a data analysis: Compare measured distributions to theoretical
More informationError Analysis and Graph Drawing
Error Analysis and Graph Drawing I. Introduction: I.1 It is impossible to do an experimental measurement with perfect accuracy. There is always an uncertainty associated with any measured quantity in an
More informationMethods and Tools of Physics
Methods and Tools of Physics Order of Magnitude Estimation: Essential idea: Scientists aim towards designing experiments that can give a true value from their measurements, but due to the limited precision
More information ± σ A ± t A ˆB ± σ B ± t B. (1)
Version 05035 Introduction Combining measurements which have theoretical uncertainties is a delicate matter. Indeed, we are often in the position in which sufficient information is not provided to form
More informationConservation of Momentum
Learning Goals Conservation of Momentum After you finish this lab, you will be able to: 1. Use Logger Pro to analyze video and calculate position, velocity, and acceleration. 2. Use the equations for 2-dimensional
More informationExperiment 2 Random Error and Basic Statistics
PHY9 Experiment 2: Random Error and Basic Statistics 8/5/2006 Page Experiment 2 Random Error and Basic Statistics Homework 2: Turn in at start of experiment. Readings: Taylor chapter 4: introduction, sections
More informationPhysics 121, Spring 2008 Mechanics. Physics 121, Spring What are we going to talk about today? Physics 121, Spring Goal of the course.
Physics 11, Spring 008 Mechanics Department of Physics and Astronomy University of Rochester Physics 11, Spring 008. What are we going to talk about today? Goals of the course Who am I? Who are you? Course
More information