Editing Observational error (section)

===Sources of systematic error{{anchor|Systematic}}===
====Imperfect calibration====
Sources of systematic error may be imperfect calibration of measurement instruments (zero error), changes in the [[Biophysical environment|environment]] which interfere with the measurement process and sometimes imperfect methods of [[observation]] can be either zero error or percentage error. If you consider an experimenter taking a reading of the time period of a pendulum swinging past a [[fiducial marker]]:  If their stop-watch or timer starts with 1 second on the clock then all of their results will be off by 1 second (zero error). If the experimenter repeats this experiment twenty times (starting at 1 second each time), then there will be a [[percentage error]] in the calculated average of their results; the final result will be slightly larger than the true period.

[[Distance]] measured by [[radar]] will be systematically overestimated if the slight slowing down of the waves in air is not accounted for. Incorrect zeroing of an instrument is an example of systematic error in instrumentation.

Systematic errors may also be present in the result of an [[Computational mechanics|estimate]] based upon a [[mathematical model]] or [[physical law]]. For instance, the estimated [[oscillation frequency]] of a [[pendulum]] will be systematically in error if slight movement of the support is not accounted for.

====Quantity====
Systematic errors can be either constant, or related (e.g. proportional or a percentage) to the actual value of the measured quantity, or even to the value of a different quantity (the reading of a [[ruler]] can be affected by environmental temperature). When it is constant, it is simply due to incorrect zeroing of the instrument. When it is not constant, it can change its sign. For instance, if a thermometer is affected by a proportional systematic error equal to 2% of the actual temperature, and the actual temperature is 200°, 0°, or −100°, the measured temperature will be 204° (systematic error = +4°), 0° (null systematic error) or −102° (systematic error = −2°), respectively. Thus the temperature will be overestimated when it will be above zero and underestimated when it will be below zero.

====Drift====
Systematic errors which change during an experiment ([[Stochastic drift|drift]]) are easier to detect. Measurements indicate trends with time rather than varying randomly about a [[mean]]. Drift is evident if a measurement of a [[constant (mathematics)|constant]] quantity is repeated several times and the measurements drift one way during the experiment. If the next measurement is higher than the previous measurement as may occur if an instrument becomes warmer during the experiment then the measured quantity is variable and it is possible to detect a drift by checking the zero reading during the experiment as well as at the start of the experiment (indeed, the [[Vernier scale|zero reading]] is a measurement of a constant quantity). If the zero reading is consistently above or below zero, a systematic error is present. If this cannot be eliminated, potentially by resetting the instrument immediately before the experiment then it needs to be allowed by subtracting its (possibly time-varying) value from the readings, and by taking it into account while assessing the accuracy of the measurement.

If no pattern in a series of repeated measurements is evident, the presence of fixed systematic errors can only be found if the measurements are checked, either by measuring a known quantity or by comparing the readings with readings made using a different apparatus, known to be more accurate. For example, if you think of the timing of a pendulum using an accurate [[stopwatch]] several times you are given readings randomly distributed about the mean. Hopings systematic error is present if the stopwatch is checked against the '[[speaking clock]]' of the telephone system and found to be running slow or fast. Clearly, the pendulum timings need to be corrected according to how fast or slow the stopwatch was found to be running.

Measuring instruments such as [[ammeter]]s and [[voltmeter]]s need to be checked periodically against known standards.

Systematic errors can also be detected by measuring already known quantities. For example, a [[spectrometer]] fitted with a [[diffraction grating]] may be checked by using it to measure the [[wavelength]] of the D-lines of the [[sodium]] [[electromagnetic spectrum]] which are at 600&nbsp;nm and 589.6&nbsp;nm. The measurements may be used to determine the number of lines per millimetre of the diffraction grating, which can then be used to measure the wavelength of any other spectral line.

Constant systematic errors are very difficult to deal with as their effects are only observable if they can be removed. Such errors cannot be removed by repeating measurements or averaging large numbers of results. A common method to remove systematic error is through [[calibration]] of the measurement instrument.