Observational error (or measurement error) is the difference between a measured value of a quantity and its unknown true value. Such errors are inherent in the measurement process; for example lengths measured with a ruler calibrated in whole centimeters will have a measurement error of several millimeters. The error or uncertainty of a measurement can be estimated and is specified with the measurement, for example, 32.3 ± 0.5 cm.
Scientific observations are marred by two distinct types of errors, systematic errors on the one hand, and random on the other hand. The effects of random errors can be mitigated by repeated measurements. Constant or systematic errors on the contrary must be carefully avoided, because they arise from one or more causes which constantly act in the same way, and have the effect of always altering the result of the experiment in the same direction. They therefore alter the value observed and repeated identical measurements do not reduce such errors.
Measurement errors can be summarized in terms of accuracy and precision.
For example, length measurements with a ruler accurately calibrated in whole centimeters will be subject to random error with each use on the same distance giving a slightly different value resulting in limited precision; a metallic ruler the temperature of which is not controlled will be affected by thermal expansion causing an additional systematic error resulting in limited accuracy.
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.
thumb|Distribution of measurements of known true value, with both constant systematic error and normally distributed random error
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 observation.
- 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, and errors due to 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.
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.
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<sup>2</sup> 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.
See also
- Bias (statistics)
- Correction for measurement error (for Pearson correlations)
- Errors and residuals in statistics
- Errors-in-variables models
- Instrument error
- Measurement uncertainty
- Metrology
- Outlier
- Regression dilution