Measurement and Experimental Error（测量和实验误差）.pdf

Measurement and Experimental Error nd References: 1) An Introduction to Error Analysis, 2 Edition, J. R. Taylor 2) Data Reduction and Error Analysis for the Physical Sciences, 2nd Edition, P. R. Bevington, D. K. Robinson 1.1 Definitions • Error analysis is the evaluation of uncertainty in measurements • Error means uncertainty, not mistake, no negative connotation. • Experimentation = measurements = comparison to a standard e.g., length, time, weight, volume, chemical composition etc. • All measurements have associated “error” or uncertainty. • Experimental results should be accompanied with best estimate of the quantity and range within which you are confident e.g., x ± Δx x = best estimate (want this to be as exact as possible) Δx = uncertainty (this is really an estimate) relative uncertainty: Δx/x • Precision: measure of how carefully the result is determined without reference to any true value (precision is related to uncertainty, e.g., Δx) • Accuracy: how close the measurement is to the exact value Example 1. Measurement of length. Questions: o Why would repeated measurements give different numbers (what is the cause) o What is the “true” length. (What actually do we mean by the length of the object; there is no such thing, only a range of lengths). o How do I report the length? o How can I minimize the “error” or uncertainty in the measurement? o One goal of an experimentalist is to minimize the uncertainties in a measurement. You should also always state how your uncertainties were calculated. Example 2. Measurement of particle number concentration with a CNC or CPC. Concentration = No. particles/volume of air