Measurement Uncertainty -- Sources and Treatment of Random Errors

Random errors in measurements are caused by unpredictable variations in the measurement system. In some books, they are known by the alternative name precision errors. Typical sources of random error are:

• measurements taken by human observation of an analogue meter, especially where this involves interpolation between scale points.

• electrical noise.

• random environmental changes, for example, sudden draught of air.

Random errors are usually observed as small perturbations of the measurement either side of the correct value, that is, positive errors and negative errors occur in approximately equal numbers for a series of measurements made of the same constant quantity. Therefore, random errors can largely be eliminated by calculating the average of a number of repeated measurements. Of course, this is only possible if the quantity being measured remains at a constant value during the repeated measurements. This averaging process of repeated measurements can be done automatically by intelligent instruments, as discussed in Section 11.

While the process of averaging over a large number of measurements reduces the magnitude of random errors substantially, it would be entirely incorrect to assume that this totally eliminates random errors. This is because the mean of a number of measurements would only be equal to the correct value of the measured quantity if the measurement set contained an infinite number of values. In practice, it’s impossible to take an infinite number of measurements. Therefore, in any practical situation, the process of averaging over a finite number of measurements only reduces the magnitude of random error to a small (but nonzero) value. The degree of confidence that the calculated mean value is close to the correct value of the measured quantity can be indicated by calculating the standard deviation or variance of data, these being parameters that describe how the measurements are distributed about the mean value (see Sections 1 and 2). This leads to a more formal quantification of this degree of confidence in terms of the standard error of the mean in Section 6.6.

NEXT: Statistical Analysis of Measurements Subject to Random Errors

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