Types of Errors Common sources of error in astronomy laboratory ...
Types of Errors Common sources of error in astronomy laboratory ...
Types of Errors Common sources of error in astronomy laboratory ...
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<strong>Types</strong> <strong>of</strong> <strong>Errors</strong><br />
Measurement <strong>error</strong>s may be classified as either random or systematic, depend<strong>in</strong>g on<br />
how the measurement was obta<strong>in</strong>ed (an <strong>in</strong>strument could cause a random <strong>error</strong> <strong>in</strong> one<br />
situation and a systematic <strong>error</strong> <strong>in</strong> another).<br />
Random <strong>error</strong>s are statistical fluctuations (<strong>in</strong> either direction) <strong>in</strong> the measured data due<br />
to the precision limitations <strong>of</strong> the measurement device. Random <strong>error</strong>s can be evaluated<br />
through statistical analysis and can be reduced by averag<strong>in</strong>g over a large number <strong>of</strong><br />
observations (see standard <strong>error</strong>).<br />
Systematic <strong>error</strong>s are reproducible <strong>in</strong>accuracies that are consistently <strong>in</strong> the same<br />
direction. These <strong>error</strong>s are difficult to detect and cannot be analyzed statistically. If a<br />
systematic <strong>error</strong> is identified when calibrat<strong>in</strong>g aga<strong>in</strong>st a standard, apply<strong>in</strong>g a correction or<br />
correction factor to compensate for the effect can reduce the bias. Unlike random <strong>error</strong>s,<br />
systematic <strong>error</strong>s cannot be detected or reduced by <strong>in</strong>creas<strong>in</strong>g the number <strong>of</strong> observations.<br />
Our strategy is to reduce as many <strong>sources</strong> <strong>of</strong> <strong>error</strong> as we can, and then to keep track <strong>of</strong><br />
those <strong>error</strong>s that we can’t elim<strong>in</strong>ate. It is useful to study the types <strong>of</strong> <strong>error</strong>s that may<br />
occur, so that we may recognize them when they arise.<br />
<strong>Common</strong> <strong>sources</strong> <strong>of</strong> <strong>error</strong> <strong>in</strong> <strong>astronomy</strong> <strong>laboratory</strong> experiments:<br />
Use the follow<strong>in</strong>g as a guide to th<strong>in</strong>k<strong>in</strong>g about <strong>sources</strong> <strong>of</strong> <strong>error</strong>. Just list<strong>in</strong>g the below<br />
terms will not receive any credit. You must expla<strong>in</strong> the source <strong>of</strong> <strong>error</strong> and how it<br />
affected your measurements.<br />
Incomplete def<strong>in</strong>ition (may be systematic or random) - One reason that it is impossible<br />
to make exact measurements is that the measurement is not always clearly def<strong>in</strong>ed. For<br />
example, if two different people measure the length <strong>of</strong> the same rope, they would<br />
probably get different results because each person may stretch the rope with a different<br />
tension. The best way to m<strong>in</strong>imize def<strong>in</strong>ition <strong>error</strong>s is to carefully consider and specify<br />
the conditions that could affect the measurement.<br />
Failure to account for a factor (usually systematic) – The most challeng<strong>in</strong>g part <strong>of</strong><br />
design<strong>in</strong>g an experiment is try<strong>in</strong>g to control or account for all possible factors except the<br />
one <strong>in</strong>dependent variable that is be<strong>in</strong>g analyzed. For <strong>in</strong>stance, you may <strong>in</strong>advertently<br />
ignore air resistance when measur<strong>in</strong>g free-fall acceleration, or you may fail to account for<br />
the effect <strong>of</strong> the Earth’s magnetic field when measur<strong>in</strong>g the field <strong>of</strong> a small magnet. The<br />
best way to account for these <strong>sources</strong> <strong>of</strong> <strong>error</strong> is to bra<strong>in</strong>storm with your peers about all<br />
the factors that could possibly affect your result. This bra<strong>in</strong>storm should be done before<br />
beg<strong>in</strong>n<strong>in</strong>g the experiment so that arrangements can be made to account for the<br />
confound<strong>in</strong>g factors before tak<strong>in</strong>g data. Sometimes a correction can be applied to a result<br />
after tak<strong>in</strong>g data to account for an <strong>error</strong> that was not detected.
Instrument resolution (random) - All <strong>in</strong>struments have f<strong>in</strong>ite precision that limits the<br />
ability to resolve small measurement differences. For <strong>in</strong>stance, a meter stick cannot<br />
dist<strong>in</strong>guish distances to a precision much better than about half <strong>of</strong> its smallest scale<br />
division (0.5 mm <strong>in</strong> this case).<br />
Physical variations (random) - It is always wise to obta<strong>in</strong> multiple measurements over<br />
the entire range be<strong>in</strong>g <strong>in</strong>vestigated. Do<strong>in</strong>g so <strong>of</strong>ten reveals variations that might otherwise<br />
go undetected. These variations may call for closer exam<strong>in</strong>ation, or they may be<br />
comb<strong>in</strong>ed to f<strong>in</strong>d an average value.<br />
Parallax (systematic or random) - This <strong>error</strong> can occur whenever there is some distance<br />
between the measur<strong>in</strong>g scale and the <strong>in</strong>dicator used to obta<strong>in</strong> a measurement. If the<br />
observer’s eye is not squarely aligned with the po<strong>in</strong>ter and scale, the read<strong>in</strong>g may be too<br />
high or low (some analog meters have mirrors to help with this alignment).<br />
Personal <strong>error</strong>s come from carelessness, poor technique, or bias on the part <strong>of</strong> the<br />
experimenter. The experimenter may measure <strong>in</strong>correctly, or may use poor technique <strong>in</strong><br />
tak<strong>in</strong>g a measurement, or may <strong>in</strong>troduce a bias <strong>in</strong>to measurements by expect<strong>in</strong>g (and<br />
<strong>in</strong>advertently forc<strong>in</strong>g) the results to agree with the expected outcome. Personal <strong>error</strong>s,<br />
sometimes called mistakes or blunders, should be avoided and corrected if discovered.<br />
The term human <strong>error</strong> should never be used when describ<strong>in</strong>g <strong>sources</strong> <strong>of</strong> <strong>error</strong>. If it<br />
was a human <strong>error</strong>, don’t be lazy, fix it!