Observational error

When either randomness or uncertainty modeled by probability theory is attributed to such errors, they are "errors" in the sense in which that term is used in statistics.

Every time a measurement is repeated, slightly different results are obtained. The common statistical model used is that the error has two additive parts:

1. Random error which may vary from observation to observation.
2. Systematic error which always occurs, with the same value, when we use the instrument in the same way and in the same case.

Some errors are not clearly random or systematic such as the uncertainty in the calibration of an instrument.

Random errors or statistical errors in measurement lead to measurable values being inconsistent between repeated measurements of a constant attribute or quantity taken. Random errors create measurement uncertainty. These errors are uncorrelated between measurements. Repeated measurements will fall in a pattern and in a large set of such measurements a standard deviation can be calculated as an estimate of the amount of statistical error.

Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Sources of systematic errors include errors in equipment calibration, uncertainty in correction terms applied during experimental analysis, and errors due to the use of approximate theoretical models. Systematic error is sometimes called statistical bias. It may often be reduced with standardized procedures.

Part of the learning process in the various sciences is learning how to use standard instruments and protocols to minimize systematic error. Over a long period of time, systematic errors in science can be resolved and become a form of "negative knowledge": scientists build up an understanding of how to avoid specific kinds of systematic errors.

When two or more observations or two or more instruments are combined, the errors in each combine. Estimates of the error in the result of such combinations depend upon the statistical characteristics of each individual measurement and on the possible statistical correlation between them.

Measurement errors can be divided into two components: random error and systematic error.

Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading. Additionally, these fluctuations may be in part due to the interference of the environment with the measurement process. Random errors show up as different results for ostensibly the same repeated measurement. They can be estimated by comparing multiple measurements and reduced by averaging multiple measurements. The concept of random error is closely related to the concept of precision. The higher the precision of a measurement instrument, the smaller the variability (standard deviation) of the fluctuations in its readings.

Systematic error is predictable and typically constant or proportional to the true value. If the cause of the systematic error can be identified, then it usually can be eliminated. Systematic errors are caused by imperfect calibration of measurement instruments or imperfect methods of observation, or interference of the surroundings with the measurement process, and always affect the results of an experiment in a predictable direction. Incorrect zeroing of an instrument is an example of systematic error in instrumentation.

The Performance Test Standard PTC 19.1-2005 "Test Uncertainty", published by the American Society of Mechanical Engineers (ASME), discusses systematic and random errors in considerable detail. In fact, it conceptualizes its basic uncertainty categories in these terms.

The term "observational error" is also sometimes used to refer to response errors and some other types of non-sampling error. In survey-type situations, these errors can be mistakes in the collection of data, including both the incorrect recording of a response and the correct recording of a respondent's inaccurate response. These sources of non-sampling error are discussed in Salant and Dillman (1994) and Bland and Altman (1996).

These errors can be random or systematic. Random errors are caused by unintended mistakes by respondents, interviewers and/or coders. Systematic error can occur if there is a systematic reaction of the respondents to the method used to formulate the survey question. Thus, the exact formulation of a survey question is crucial, since it affects the level of measurement error. Different tools are available for the researchers to help them decide about this exact formulation of their questions, for instance estimating the quality of a question using MTMM experiments. This information about the quality can also be used to correct for measurement error.

If the dependent variable in a regression is measured with error, regression analysis and associated hypothesis testing are unaffected, except that the R² will be lower than it would be with perfect measurement.

However, if one or more independent variables are measured with error, then the regression coefficients and standard hypothesis tests are invalid. This is known as attenuation bias.