All readings, data, results or other numerical quantities taken from the real world by direct measurement or otherwise are subject to uncertainty. This is a consequence of not being able to measure anything exactly. Uncertainty cannot be avoided but it can be reduced by using 'better' apparatus. The uncertainty on a measurement has to do with the precision or resolution of the measuring instrument. When results are analyses it is important to consider the affects of uncertainty in subsequent calculations involving the measured quantities.If you are unlucky (or careless) then your results will also be subject to errors. Errors are mistakes in the readings that, had the experiment been done differently, been avoided. It is perfectly possible to take a measurement accurately and erroneously! Unfortunately it is not always possible to know when you are making an error (otherwise you wouldn't make it!) and so good experimental technique has to able to guard against the affect of errors and types of Error:
Human Error: Errors introduced by basic incompetence, mistakes in using the apparatus etc. Reduced by repeating the experiment several times and comparing results to those of other similar experiments, by ensuring results seem reasonable
Systematic Error: Error introduced by poor calibration or zero point setting of instruments such as meters - this may cause instrumentation to always 'under read' or 'over read' a value by a fixed amount. Reduced by plotting graphs, the relationships between two quantities often depends on the way in which they change rather than their absolute values. A systematic error would manifest itself as an intercept on the y-axis other than that expected. In the A Level course this is most commonly experienced with micrometers (that don't read zero when nothing is between the jaws) and electrical meters that may not rest at zero
Equipment Error: Error introduced by the mis-functioning of equipment. The only real check is to see if the results seem reasonable and 'make sense' ... take time to stop and think about what the instruments are telling you ... does it seem okay?
Parallax Error: Error introduced by reading scales from the wrong angle i.e. any angle other than at right angles! Some meters have mirrors to help avoid parallax error but the only real way to avoid parallax error is to be aware of it
Estimating uncertainty Estimating the uncertainty on a reading is an art that develops with experience. There are two rules of thumb:Firstly, take repeat readings. If there is a spread of readings then the uncertainty can be derived from the size of the spread of values. What you are doing in effect is seeing how repeatable the results are and this will give an order of magnitude idea of the uncertainty likely on any given reading. (See the section on dealing with averages below). For example, if three readings of time are 42s, 47s and 38s then the average is just over 42s with the other two readings being about 4s away from the average ... so use 42s ± 4s. The uncertainty is taken as 4sSecondly, if the results are repeatable to the precision of the measuring apparatus then the uncertainty is taken as half of the smallest reading possible. For example, when measuring something with a ruler marked off in mm, the uncertainty is ± 0.5mm. When using a normal protractor the uncertainty on the angle is ± 0.5 degrees etcIf the experiment generates many repeat readings (as any really good experiment should) then there is a way to analyses the results and obtain a good value for the associated uncertainty:
Take an average of the results
Work out the deviation of each result from the average
Average the deviations (ignore any minus signs) - this is the uncertainty
Human Error: Errors introduced by basic incompetence, mistakes in using the apparatus etc. Reduced by repeating the experiment several times and comparing results to those of other similar experiments, by ensuring results seem reasonable
Systematic Error: Error introduced by poor calibration or zero point setting of instruments such as meters - this may cause instrumentation to always 'under read' or 'over read' a value by a fixed amount. Reduced by plotting graphs, the relationships between two quantities often depends on the way in which they change rather than their absolute values. A systematic error would manifest itself as an intercept on the y-axis other than that expected. In the A Level course this is most commonly experienced with micrometers (that don't read zero when nothing is between the jaws) and electrical meters that may not rest at zero
Equipment Error: Error introduced by the mis-functioning of equipment. The only real check is to see if the results seem reasonable and 'make sense' ... take time to stop and think about what the instruments are telling you ... does it seem okay?
Parallax Error: Error introduced by reading scales from the wrong angle i.e. any angle other than at right angles! Some meters have mirrors to help avoid parallax error but the only real way to avoid parallax error is to be aware of it
Estimating uncertainty Estimating the uncertainty on a reading is an art that develops with experience. There are two rules of thumb:Firstly, take repeat readings. If there is a spread of readings then the uncertainty can be derived from the size of the spread of values. What you are doing in effect is seeing how repeatable the results are and this will give an order of magnitude idea of the uncertainty likely on any given reading. (See the section on dealing with averages below). For example, if three readings of time are 42s, 47s and 38s then the average is just over 42s with the other two readings being about 4s away from the average ... so use 42s ± 4s. The uncertainty is taken as 4sSecondly, if the results are repeatable to the precision of the measuring apparatus then the uncertainty is taken as half of the smallest reading possible. For example, when measuring something with a ruler marked off in mm, the uncertainty is ± 0.5mm. When using a normal protractor the uncertainty on the angle is ± 0.5 degrees etcIf the experiment generates many repeat readings (as any really good experiment should) then there is a way to analyses the results and obtain a good value for the associated uncertainty:
Take an average of the results
Work out the deviation of each result from the average
Average the deviations (ignore any minus signs) - this is the uncertainty
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