Experimental uncertainty and error
It is important not to confuse the terms ‘error’ and ‘uncertainty’, which are not synonyms. It is also important not to confuse ‘error’ with ‘mistake’ or ‘personal error’. Error, from a scientific measurement perspective, is the difference between the measured value and the true value of what is being measured. Uncertainty is a quantification of the doubt associated with a measurement result.
Experimental uncertainties are inherent in the measurement process and cannot be eliminated simply by repeating the experiment no matter how carefully it is done. There are two sources of experimental uncertainties: systematic effects and random effects. Experimental uncertainties are distinct from personal errors.
Personal errors include mistakes or miscalculations such as measuring a height when the depth should have been measured, or misreading the scale on a thermometer, or measuring the voltage across the wrong section of an electric circuit, or forgetting to divide the diameter by two before calculating the area of a circle using the formula
r2. Personal errors can be eliminated by performing the experiment again correctly the next time, and do not form part of an analysis of uncertainties.
Systematic errors are errors that affect the accuracy of a measurement. Systematic errors cause readings to differ from the true value by a consistent amount each time a measurement is made, so that all the readings are shifted in one direction from the true value. The accuracy of measurements subject to systematic errors cannot be improved by repeating those measurements.
Common sources of systematic errors include: faulty calibration of measuring instruments (and uncalibrated instruments) that consistently give the same inaccurate reading for the same value being measured), poorly maintained instruments (which may also have high random errors), or faulty reading of instruments by the user (for example, ‘parallax error’).
Random errors affect the precision of a measurement and are always present in measurements (except for ‘counting’ measurements). These types of errors are unpredictable variations in the measurement process and result in a spread of readings.
Common sources of random errors are variations in estimating a quantity that lies between the graduations (lines) on a measuring instrument, the inability to read an instrument because the reading fluctuates during the measurement and making a quick judgment of a transient event, for example, the rebound height of a ball.
The effect of random errors can be reduced by making more or repeated measurements and calculating a new mean and/or by refining the measurement method or technique.
Readings that lie a long way from other results are sometimes called outliers. Outliers should be further analysed and accounted for, rather than being automatically dismissed. Extra readings may be useful in further examining an outlier.