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Unformatted text preview: Error analysis for labs: some background PHY 252, Fall 2009 As you probably have learned by now, physics gives particular meanings to certain terms asso- ciated with error analyis: Error or uncertainty refers to the best estimate of the quantitative range within which one can trust his or her results. The error can be calculated even if there is no “official” accepted value for what is being measured. To John Q. Public, “error” refers to how badly he screwed up, or how far off his answer is from the “official” value. Systematic error refers to an error that is consistent from measurement to measurement. For example, if you always round down to the nearest tic mark on a meter stick when measuring length, you will make a systematic error of measuring a slightly shorter length. Random error refers to an error which fluctuates in an unpredictable fashion from measure- ment to measurement. For example, if you were asked to determine the number of births per day at Stony Brook University Hospital, you would likely get a slightly different number each day you inquired even though the total number of births per year might remain fairly steady from year to year. Accuracy refers to the degree to which our value is correct within uncertainty. This is largely a matter of having the correct calibration of all of our reference measurements. That is, if someone gave us a miscalibrated meter stick that was shorter than the official length of a meter, we might measure the length of a table with great precision (lots of decimal places) but poor accuracy (what we think is a meter is not really a meter). Precision can be thought of as the number of meaningful digits to a measurement. A mea- surement of a length as being 1.03424 meters is more precise than a measurement of 1.03 meters; however, if the measurement was made with an incorrectly calibrated meterstick, the measurement will have high precision but low accuracy! Reference standard is the thing that you measure against. For example, if we’re measuring the length of various tables, we might use a meter stick for the measurement. The meter stick is then our reference standard for the measurements of the lengths of the tables, and if our reference standard is inaccurate, then all measurements made using it will also be inaccurate 1 no matter how precise they are. The international system of units, or SI units (for Le Syst‘eme International d’Unit´es ), tries as much as possible to use reference standards based on natural phenomena that anyone can replicate in a properly-equipped lab (mass is the glaring excep- tion to this principle; mass is defined relative to a particular platinum-iridium cylinder sitting in Paris). The base units are a choice of seven well-defined units which by convention are regarded as dimensionally independent: the metre, the kilogram, the second, the ampere, the kelvin, the mole, and the candela. As an example, the SI unit definition of the second is as follows: The second is the duration of 9 192 631 770 periods of the radiation corresponding...
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