In September, I spent time pondering the term "precision". Since then, I have been considering some of the other HSW glossary terms also.
I understand that the ASE and the Nuffield Foundation have recently produced a book as guidance, but I don't think it proper that teachers should have to pay £10 to read about things demanded by an exam specification. I am afraid that I haven't read it — but would be very interested in the opinions of anyone who has.
Hopefully, the new exam specifications will include proper guidance/clarification, but, once more, I am deeply frustrated that such things will be foisted upon science teachers without any widespread canvassing of our opinion on the matter — especially after the debacle that we had to wade through last time.
So, here are my initial thoughts on some words that perhaps should be taught at GCSE as part of HSW. I would be most grateful for comments to correct mistakes, suggest improvements, make additions or suggest subtractions.
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Accuracy
In principle, accuracy describes the closeness of a measurement to the “true” value. However, as the “true” value is unknowable in practice, accuracy is more useful when thought of as closeness of a measurement to the “value currently accepted by the scientific community”. Even more usefully, “accurate” is a relative term – one measurement is more accurate than another if it has a smaller error.
Error
Anything that causes a measurement to not represent the true value is an error. Errors come in two categories – random and systematic.
Random errors are beyond the control of the experimenter and cannot be prevented (although they can often be reduced in size). Their effect is that sometimes the measured value with be slightly too high and sometimes slightly too low. Due to their random nature, random errors can be removed by taking the mean of many repeated measurements (as long as they agree). An example of random errors affecting a measurement is small variations in humidity, temperature or air movement affecting the rate of evaporation of water over short periods of time.
Systematic errors are artefacts of a flawed experimental method and are therefore, almost by definition, something that the experimenter is completely unaware of. The error will always be “in the same direction” (the measured value will either be consistently too high or consistently too low) and therefore averaging repeated measurements will not remove systematic errors from data. The best way to guard against systematic errors is to have someone else measure the same quantity and compare the two values, in the hope that they spot any oversights made. This cannot guarantee the elimination of systematic error but does increase the reliability of the measured value and conclusions based upon it. An example of systematic errors affecting a measurement is not removing shoes/standing straight/etc when measuring a person’s height.
Measurement precision
Any method of measuring that, when repeated, produces similar data over and over again is referred to as precise. Reducing random errors is the most straight-forward way of improving the precision of an experiment. Note, however, that systematic errors may still exist even in precise measurement methods and so precision has no bearing at all on accuracy. More precise experimental methods also result in greater reliability of measured values and conclusions based upon them.
The use of the word “precision” above, in the context of an experimental procedure, is unfortunate and confusing, as the word has an everyday meaning in the context of a single measured value. A single value is precise if it is quoted to many significant figures – ie it has a small uncertainty in its value (this has nothing to do with error). For example, 3.4m refers to an actual length between 3.35m and 3.45m. The uncertainty in the measurement is 0.1m. Compare this to the “more precise” value 3.42m, which limits the actual value to being between 3.415m and 3.425m, an uncertainty of just 0.01m. Improving the precision of measured values is most easily done by using more sensitive measuring devices – ie ones with finer scale divisions (higher resolution).
The two “precisions” are tenuously related — but must never be confused. To illustrate the loose connection, consider the fact that if individual measured values are precise (ie made with sensitive, high resolution measuring devices), smaller random errors will be more apparent and therefore greater efforts will have to be made to reduce them in order to achieve measurement precision. Precise values thus drive a push for a higher level of measurement precision.
The perfect experiment
Ideally, experimental methods will be constructed without systematic errors and steps will be taken to deal with random errors (for example, but not limited to, through the averaging of repeated measurements of the same value). Such methods will then be precise (return the same answers every time) and produce data that is both accurate (close to the true value) and reliable (unlikely to be wrong).