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: • Random error which may vary from observation to another. • 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. Sources of systematic errors include errors in equipment calibration, uncertainty in correction terms applied during experimental analysis, errors due the use of approximate theoretical models. == Propagation of 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. == Characterization ==

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 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. ==Sources ==

The term "observational error" is also sometimes used to refer to response errors and some other types of non-sampling error. 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 in order to correct for measurement error. ==Effect on regression analysis==

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 is measured with error, then the regression coefficients and standard hypothesis tests are invalid. This is known as attenuation bias. ==See also==