Random Error Analysis
Contents |
it. In doing this it is crucial to understand that all measurements of physical quantities are subject to uncertainties. It is never possible random error calculation to measure anything exactly. It is good, of course, to make the
Random Error Examples
error as small as possible but it is always there. And in order to draw valid conclusions the how to reduce random error error must be indicated and dealt with properly. Take the measurement of a person's height as an example. Assuming that her height has been determined to be 5' 8", how
Systematic Error Calculation
accurate is our result? Well, the height of a person depends on how straight she stands, whether she just got up (most people are slightly taller when getting up from a long rest in horizontal position), whether she has her shoes on, and how long her hair is and how it is made up. These inaccuracies could all be called random error examples physics errors of definition. A quantity such as height is not exactly defined without specifying many other circumstances. Even if you could precisely specify the "circumstances," your result would still have an error associated with it. The scale you are using is of limited accuracy; when you read the scale, you may have to estimate a fraction between the marks on the scale, etc. If the result of a measurement is to have meaning it cannot consist of the measured value alone. An indication of how accurate the result is must be included also. Indeed, typically more effort is required to determine the error or uncertainty in a measurement than to perform the measurement itself. Thus, the result of any physical measurement has two essential components: (1) A numerical value (in a specified system of units) giving the best estimate possible of the quantity measured, and (2) the degree of uncertainty associated with this estimated value. For example, a measurement of the width of a table would yield a result such as 95.3 +/- 0.1 cm. Significant Figures The significan
just how much the measured value is likely to deviate from the unknown, true, value of the quantity. The art of estimating these deviations should probably be called uncertainty analysis, but for historical reasons is referred to as error
How To Reduce Systematic Error
analysis. This document contains brief discussions about how errors are reported, the kinds of errors that
Personal Error
can occur, how to estimate random errors, and how to carry error estimates into calculated results. We are not, and will not be, concerned with zero error the “percent error” exercises common in high school, where the student is content with calculating the deviation from some allegedly authoritative number. Significant figures Whenever you make a measurement, the number of meaningful digits that you write down implies the http://teacher.nsrl.rochester.edu/phy_labs/AppendixB/AppendixB.html error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant http://www.owlnet.rice.edu/~labgroup/pdf/Error_analysis.htm figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m. Students frequently are confused about when to count a zero as a significant figure. The rule is: If the zero has a non-zero digit anywhere to its left, then the zero is significant, otherwise it is not. For example 5.00 has 3 significant figures; the number 0.0005 has only one significant figure, and 1.0005 has 5 significant figures. A number like 300 is not well defined. Rather one should write 3 x 102, one significant figure, or 3.00 x 102, 3 significant figures. Absolute and relative errors The absolute error in a measured quantity is the uncertainty in the quantity and has the same units as the quantity itself. For example if you know a length is 0.428 m ± 0.002 m, the 0.002 m is an absolute error. The relative error (also called the fractional error) is obtained by dividing the absolute error in the quantity by the quantity itself. The relative error is usually more si
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