Observational error - wikipedia Observational error `` Systematic bias '' redirects here. This article is about the metrology and statistical topic. For the sociological and organizational phenomenon, see systemic bias. `` Measurement error '' redirects here. It is not to be confused with Measurement uncertainty. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. ( September 2016 ) Observational error ( or measurement error ) is the difference between a measured value of a quantity and its true value. In statistics, an error is not a `` mistake ''. Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components : random error and systematic error. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy ( involving either the observation or measurement process ) inherent to the system. Systematic error may also refer to an error with a nonzero mean, the effect of which is not reduced when observations are averaged. Contents 1 Science and experiments 2 Random errors versus systematic errors 3 Sources of systematic error 3.1 Imperfect calibration 3.2 Quantity 3.3 Drift 4 Sources of random error 5 Surveys 6 Effect on regression analysis 7 See also 8 Further reading 9 References Science and experiments 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 ; see errors and residuals in statistics. Every time we repeat a measurement with a sensitive instrument, we obtain slightly different results. The common statistical model used is that the error has two additive parts : systematic error which always occurs, with the same value, when we use the instrument in the same way and in the same case, and random error which may vary from observation to another. 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 so as to minimize systematic error. Random error ( or random variation ) is due to factors which can not or will not be controlled. Some possible reason to forgo controlling for these random errors is because it may be too expensive to control them each time the experiment is conducted or the measurements are made. Other reasons may be that whatever we are trying to measure is changing in time ( see dynamic models ), or is fundamentally probabilistic ( as is the case in quantum mechanics -- see Measurement in quantum mechanics ). Random error often occurs when instruments are pushed to the extremes of their operating limits. For example, it is common for digital balances to exhibit random error in their least significant digit. Three measurements of a single object might read something like 0.9111 g, 0.9110 g, and 0.9112 g. Random errors versus systematic errors 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. 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. Systematic error, however, 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 environment with the measurement process, and always affect the results of an experiment in a predictable direction. Incorrect zeroing of an instrument leading to a zero error 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. Random error can be caused by unpredictable fluctuations in the readings of a measurement apparatus, or in the experimenter 's interpretation of the instrumental reading ; these fluctuations may be in part due to interference of the environment with the measurement process. 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. Sources of systematic error Imperfect calibration Sources of systematic error may be imperfect calibration of measurement instruments ( zero error ), changes in the 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 leading to a zero error is an example of systematic error in instrumentation. Systematic errors may also be present in the result of an 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 ( 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 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 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 can not 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. A 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 ammeters and voltmeters 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 nm and 589.6 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 can not 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. Sources of random error The random or stochastic error in a measurement is the error that is random from one measurement to the next. Stochastic errors tend to be normally distributed when the stochastic error is the sum of many independent random errors because of the central limit theorem. Stochastic errors added to a regression equation account for the variation in Y that can not be explained by the included Xs. Surveys 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 ( 1995 ) 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 or predicting this quality using the Survey Quality Predictor software ( SQP ). 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 R 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. See also Correction for measurement error ( for Pearson correlations ) Errors and residuals in statistics Error Replication ( statistics ) Statistical theory Metrology Regression dilution Test method Propagation of uncertainty Instrument error Measurement uncertainty Errors - in - variables models Systemic bias Further reading Errors of Measurement in Statistics, W.G. Cochran, Technometrics, Vol. 10, No. 4 ( Nov., 1968 ), pp. 637 -- 666 References ^ Jump up to : Dodge, Y. ( 2003 ) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0 - 19 - 920613 - 9 ^ Jump up to : John Robert Taylor ( 1999 ). An Introduction to Error Analysis : The Study of Uncertainties in Physical Measurements. University Science Books. p. 94, § 4.1. ISBN 0 - 935702 - 75 - X. Jump up ^ `` Systematic error ''. Merriam-webster.com. Retrieved 2016 - 09 - 10. Jump up ^ `` Google ''. Google.com. Retrieved 2016 - 09 - 10. Jump up ^ Salant, P., and D.A. Dillman. `` How to conduct your survey. '' ( 1994 ). Jump up ^ Bland, J. Martin, and Douglas G. Altman. `` Statistics notes : measurement error. '' Bmj 313.7059 ( 1996 ) : 744. Jump up ^ Saris, W.E. and Gallhofer, I.N. ( 2014 ). Design, evaluation and analysis of questionnaires for survey research. Second Edition. Hoboken, Wiley. Jump up ^ DeCastellarnau, A. and Saris, W.E. ( 2014 ). A simple procedure to correct for measurement errors in survey research. European Social Survey Education Net ( ESS EduNet ). Available at : http://essedunet.nsd.uib.no/cms/topics/measurement Jump up ^ Saris, W.E. ; Revilla, M. ( 2015 ). `` Correction for measurement errors in survey research : necessary and possible ''. Social Indicators Research. 127 : 1005 -- 1020. doi : 10.1007 / s11205 - 015 - 1002 - x. Jump up ^ Hayashi, Fumio ( 2000 ). Econometrics. Princeton University Press. ISBN 0 - 691 - 01018 - 8. Jump up ^ W.G. Cochran ( November 1968 ). `` Errors of Measurement in Statistics ''. Technometrics. Taylor & Francis, Ltd. on behalf of American Statistical Association and American Society for Quality. 10 : 637 -- 666. doi : 10.2307 / 1267450. JSTOR 1267450. Retrieved from `` https://en.wikipedia.org/w/index.php?title=Observational_error&oldid=850037426 '' Categories : Accuracy and precision Errors and residuals Hidden categories : Articles needing additional references from September 2016 All articles needing additional references Talk Contents About Wikipedia Беларуская Беларуская ( тарашкевіца ) ‎ Català Čeština Deutsch Ελληνικά Español Euskara فارسی Français Italiano Lietuvių Polski Português Română Русский Српски / srpski Suomi Svenska Українська 中文 13 more Edit links This page was last edited on 13 July 2018, at 04 : 43 ( UTC ). Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: errors that consistently cause measurement value to be too large or too small
Answer: Systematic errors