Physics: Sources of Errors
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 that may come from a variety of sources. The process of evaluating this uncertainty associated with a measurement result is often called uncertainty analysis or error analysis.
The complete statement of a measured value should include an estimate of the level of confidence associated with the value. Properly reporting an experimental result along with its uncertainty allows other people to make judgements about the quality of the experiment, and it facilitates meaningful comparisons with other similar values or a theoretical prediction. Without an uncertainty estimate, it is impossible to answer the basic scientific question: "Does my result agree with a theoretical prediction or results from other experiments?" This question is fundamental for deciding if a scientific hypothesis is confirmed or refuted.
When we make a measurement, we generally assume that some exact or true value exists based on how we define what is being measured. While we may never know this true value exactly, we attempt to find this ideal quantity to the best of our ability with the time and resources available. As we make measurements by different methods, or even when making multiple measurements using the same method, we may obtain slightly different results. So how do we report our findings for our best estimate of this elusive true value? The most common way to show the range of values that we believe includes the true value is: measurement = best estimate uncertainty
Let�s take an example. Suppose you want to find the mass of a gold ring that you would like to sell to a friend. You do not want to jeopardize your friendship, so you want to get an accurate mass of the ring in order to charge a fair market price. By simply examining the ring in your hand, you estimate the
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 that may come from a variety of sources. The process of evaluating this uncertainty associated with a measurement result is often called uncertainty analysis or error analysis.
The complete statement of a measured value should include an estimate of the level of confidence associated with the value. Properly reporting an experimental result along with its uncertainty allows other people to make judgements about the quality of the experiment, and it facilitates meaningful comparisons with other similar values or a theoretical prediction. Without an uncertainty estimate, it is impossible to answer the basic scientific question: "Does my result agree with a theoretical prediction or results from other experiments?" This question is fundamental for deciding if a scientific hypothesis is confirmed or refuted.
When we make a measurement, we generally assume that some exact or true value exists based on how we define what is being measured. While we may never know this true value exactly, we attempt to find this ideal quantity to the best of our ability with the time and resources available. As we make measurements by different methods, or even when making multiple measurements using the same method, we may obtain slightly different results. So how do we report our findings for our best estimate of this elusive true value? The most common way to show the range of values that we believe includes the true value is: measurement = best estimate uncertainty
Let�s take an example. Suppose you want to find the mass of a gold ring that you would like to sell to a friend. You do not want to jeopardize your friendship, so you want to get an accurate mass of the ring in order to charge a fair market price. By simply examining the ring in your hand, you estimate the
References: Taylor, John. An Introduction to Error Analysis, 2nd. ed. University Science Books: Sausalito, 1997. Baird, D.C. Experimentation: An Introduction to Measurement Theory and Experiment Design, 3rd. ed. Prentice Hall: Englewood Cliffs, 1995. Bevington, Phillip and Robinson, D. Data Reduction and Error Analysis for the Physical Sciences, 2nd. ed. McGraw-Hill: New York, 1991. ISO. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization (ISO) and the International Committee on Weights and Measures (CIPM): Switzerland, 1993. NIST. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, 1994. Available online: http://physics.nist.gov/Pubs/guidelines/contents.html Copyright: The University of North Carolina at Chapel Hill, Department of Physics and Astronomy Last revised: August 10, 2000 by Duane Deardorff, Director of Undergraduate Laboratories