# What are systematic errors and random errors

### Random and systematic errors

Author: Hans Lohninger

Mistakes happen when measuring data. These errors can be divided into three categories:

• systematic errors: Errors that arise because, for example, a measuring device is incorrectly calibrated or the samples are contaminated. Systematic errors are expressed in an (often) constant or proportional shift in the measured values. Systematic errors affect the accuracy, they can both add up and cancel each other out.
• random errors: arise from random processes during the measurement, e.g. the thermal noise of the sensor or the quantization noise. Random errors affect the precision of a measurement and always add up (see error propagation law).
• Runaway: are individual values ​​that are far outside the usual measured values. Rough outliers can be easily identified and removed.

The easiest way to do this is accuracy and precision imagine at a darts game. If the player has a high degree of correctness, he hits the bull's eye on average. However, this is of little help if the precision of his throws is poor. Conversely, a player with a steady hand can achieve very good precision and still hit the center of the target permanently.

 Left: High accuracy with high precision. Middle: High accuracy with low precision. Right: Low accuracy with high precision. Obviously a systematic error occurs here. Click on the picture to start an interactive example.

If this distinction between correctness and precision is transferred to statistics, it is obvious that the correctness of a measurement can be described by the mean value (or in general any measure of the position of the distribution of the measured values), the precision by the standard deviation (or by another spread).(1)

#### Examples of systematic errors

Reference error:
• Incorrect calibration: Calibration errors can produce both an additive and a multiplicative error.
• Volume-dependent references, such as volumetric flasks, used at the wrong temperature.
• Thermocouples always provide the difference between the measuring point and the cold point as the temperature value; if the cold junction drifts, this also changes the measured value.
• The aging of sensors can lead to a shift in the calibration
Method error:
• Detection reactions, the end point of which is not reached in time (equilibrium is never established due to the slow kinetics).
• Instability best. Species can cause the signal to change during the measurement.
• Cross-sensitivities are a general problem that can have serious effects, especially when measuring in highly complex matrices.
• personal errors mostly stem from preferences or peculiarities of the person measuring. Operator and laboratory performance can be determined using round robin tests.