Measurement errors and their classification

Date: 2015-10-07; view: 420.

THEORY

Two terms are widely used in discussions of the reliability of data: precisionandaccuracy.

Precision describes the reproducibility of results, that is, the agreement between numerical values for two or more replicate measurements, or measurements that have been made in exactly the same way. Generally, the precision of an analytical method is readily obtained by simply repeating the measurement. [Two] terms are used to describe the precision of a set of replicate data: standard deviation [and] variance. These terms have statistical significance.

Accuracy describes the correctness of an experimental result expressed as the closeness of the measurement to the true or accepted value. Accuracy is expressed in terms of either absolute errororrelative error.

Assume that the true value of a quantity is x₀. By measuring this value tend to get a result different from x₀. If the measurement is performed repeatedly, the measurement is not only different from x₀, but in most cases are different and each other. Denote measurements x₁, x₂, x₃, ..., x_n, then the difference

Δ x_i = x_i - x₀, where i = 1, 2, ..., n, (1)

is called the absolute error of measurement. It is expressed in units of the measured value.

The accuracy in terms of the relative error E_r equals to

In the classification of errors according to their properties distinguish systematic errors, random errorsandmisses.

Systematic errors in experimental observations usually come from the measuring instruments. They may occur because:

· there is something wrong with the instrument or its data handling system, or

· because the instrument is wrongly used by the experimenter.

Random errors in experimental measurements are caused by unknown and unpredictable changes in the experiment. These changes may occur in the measuring instruments or in the environmental conditions, for example: temperature, pressure, humidity.

Misses - a consequence of wrong actions of the experimenter. This, for example, incorrect recording of the results of observation, wrong metering, etc. If you notice misses they will be excluded from the calculations.