Errors during the measurement process

Rogue data points

In a set of measurements subject to random error, measurements with a very large error sometimes occur at random and unpredictable times, where the magnitude of the error is much larger than could reasonably be attributed to the expected random varia[1]tions in measurement value. Sources of such abnormal error include sudden transient voltage surges on the mains power supply and incorrect recording of data (e.g. writing down 146.1 when the actual measured value was 164.1). It is accepted practice in such cases to discard these rogue 

measurements, and a threshold level of a š3 deviation is often used to determine what should be discarded. It is extremely rare for measure[1]ment errors to exceed š3 limits when only normal random effects are affecting the measured value.

Special case when the number of measurements is small

When the number of measurements of a quantity is particularly small and statistical analysis of the distribution of error values is required, problems can arise when using standard Gaussian tables in terms of z as defined in equation (3.16) because the mean of only a small number of measurements may deviate significantly from the true measure[1]ment value. In response to this, an alternative distribution function called the Student-t distribution can be used which gives a more accurate prediction of the error distribution when the number of samples is small. This is discussed more fully in Miller (1990).

3.6 Aggregation of measurement system errors

Errors in measurement systems often arise from two or more different sources, and these must be aggregated in the correct way in order to obtain a prediction of the total likely error in output readings from the measurement system. Two different forms of aggregation are required. Firstly, a single measurement component may have both systematic and random errors and, secondly, a measurement system may consist of several measurement components that each have separate errors.

3.6.1 Combined effect of systematic and random errors

If a measurement is affected by both systematic and random errors that are quantified as ±x (systematic errors) and ±y (random errors), some means of expressing the combined effect of both types of error is needed. One way of expressing the combined error would be to sum the two separate components of error, i.e. to say that the total possible error is e = ±(x + y). However, a more usual course of action is to express the likely maximum error as follows:

It can be shown (ANSI/ASME, 1985) that this is the best expression for the error statistically, since it takes account of the reasonable assumption that the systematic and random errors are independent and so are unlikely to both be at their maximum or minimum value at the same time.