偶然誤差

関: accidental error

WordNet

(baseball) a failure of a defensive player to make an out when normal play would have sufficed (同)misplay
departure from what is ethically acceptable (同)wrongdoing
(computer science) the occurrence of an incorrect result produced by a computer (同)computer error
a misconception resulting from incorrect information (同)erroneous belief
part of a statement that is not correct; "the book was full of errors" (同)mistake
lacking any definite plan or order or purpose; governed by or depending on chance; "a random choice"; "bombs fell at random"; "random movements"
to make a mistake or be incorrect (同)mistake, slip
the basic unit of money in South Africa; equal to 100 cents

PrepTutorEJDIC

〈C〉『誤り』,『まちがい』 / 〈U〉思い違い,誤解 / 〈U〉〈C〉過ち,過失 / 〈U〉(計数の)誤差 / 〈C〉(野球で)エラー,失策
『手当たりしだいの』,任意の;行き当たりばったりの
(判断・考え方・選択などで)『誤る』,まちがえる;過ちを犯す,罪を犯す《+『in』+『名』(do『ing』)》 / (正道・目的などから)それる,逸脱する《+『from』+『名』》
ラント(南アフリカ共和国の通貨の単位)

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/05/26 16:19:40」(JST)

wiki en

[Wiki en表示]

A scientist adjusts an atomic force microscopy (AFM) device, which is used to measure surface characteristics and imaging for semiconductor wafers, lithography masks, magnetic media, CDs/DVDs, biomaterials, optics, among a multitude of other samples.

Observational error (or measurement error) is the difference between a measured value of quantity and its true value.^[1] In statistics, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.

Measurement errors can be divided into two components: random error and systematic error.^[2] Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy (as of observation or measurement) inherent in the system.^[3] Systematic error may also refer to an error having a nonzero mean, so that its effect is not reduced when observations are averaged.^[4]

Overview

There are two types of measurement error: systematic errors and random errors.

A systematic error (an estimate of which is known as a measurement bias) is associated with the fact that a measured value contains an offset. In general, a systematic error, regarded as a quantity, is a component of error that remains constant or depends in a specific manner on some other quantity.

A random error is associated with the fact that when a measurement is repeated it will generally provide a measured value that is different from the previous value. It is random in that the next measured value cannot be predicted exactly from previous such values. (If a prediction were possible, allowance for the effect could be made.)

In general, there can be a number of contributions to each type of error.

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 we use 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 observation.

Systematic error is sometimes called statistical bias. It may often be reduced by very carefully standardized procedures. Part of the education in every science is how to use the standard instruments of the discipline.

The random error (or random variation) is due to factors which we cannot (or do not) control. It may be too expensive or we may be too ignorant of these factors to control them each time we measure. It may even 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 their 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 0.9111g, 0.9110g, and 0.9112g.

Systematic versus random error

Measurement errors can be divided into two components: random error and systematic error.^[2]

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 errors lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken. The word random indicates that they are inherently unpredictable, and have null expected value, namely, they are scattered about the true value, and tend to have null arithmetic mean when a measurement is repeated several times with the same instrument. All measurements are prone to random error. Because random errors are reduced by re-measurement (making n times as many independent measurements will usually reduce random errors by a factor of √n), it is worth repeating an experiment until random errors are similar in size to systematic errors. Additional measurements will be of little benefit, because the overall error cannot be reduced below the systematic error.

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 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. 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 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.

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 cannot 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.^[1] 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)^[5] and Bland and Altman (1996).^[6]

References

^ ^a ^b Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
^ ^a ^b 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.
^ http://www.merriam-webster.com/dictionary/systematic%20error
^ https://www.google.com/webhp?sourceid=chrome-instant&rlz=1CASMAG_enUS602US603&ion=1&espv=2&ie=UTF-8#q=systematic%20error%20definition
^ Salant, P., and D. A. Dillman. "How to conduct your survey." (1994).
^ Bland, J. Martin, and Douglas G. Altman. "Statistics notes: measurement error." Bmj 313.7059 (1996): 744.

Errors of Measurement in Statistics, W. G. Cochran, Technometrics, Vol. 10, No. 4 (Nov., 1968), pp. 637–666: http://www.jstor.org/stable/1267450

UpToDate Contents

全文を閲覧するには購読必要です。 To read the full text you will need to subscribe.

1. システマティックレビューおよびメタアナリシス systematic review and meta analysis
2. 証拠、p値、および仮説検定 proof p values and hypothesis testing
3. 胎児体重の出生前超音波評価 prenatal sonographic assessment of fetal weight
4. 原発性（本態性）高血圧の病因における低出生体重の潜在的役割 possible role of low birth weight in the pathogenesis of primary essential hypertension
5. エビデンスに基づいた医療 evidence based medicine

English Journal

Evaluation of overall setup accuracy and adequate setup margins in pelvic image-guided radiotherapy: Comparison of the male and female patients.

Laaksomaa M1, Kapanen M2, Tulijoki T3, Peltola S2, Hyödynmaa S2, Kellokumpu-Lehtinen PL3.Author information 1Department of Oncology, Tampere University Hospital (TAUH), Tampere, Finland. Electronic address: marko.laaksomaa@pshp.fi.2Department of Oncology, Tampere University Hospital (TAUH), Tampere, Finland; Department of Medical Physics, Tampere University Hospital (TAUH), Tampere, Finland.3Department of Oncology, Tampere University Hospital (TAUH), Tampere, Finland.AbstractWe evaluated adequate setup margins for the radiotherapy (RT) of pelvic tumors based on overall position errors of bony landmarks. We also estimated the difference in setup accuracy between the male and female patients. Finally, we compared the patient rotation for 2 immobilization devices. The study cohort included consecutive 64 male and 64 female patients. Altogether, 1794 orthogonal setup images were analyzed. Observer-related deviation in image matching and the effect of patient rotation were explicitly determined. Overall systematic and random errors were calculated in 3 orthogonal directions. Anisotropic setup margins were evaluated based on residual errors after weekly image guidance. The van Herk formula was used to calculate the margins. Overall, 100 patients were immobilized with a house-made device. The patient rotation was compared against 28 patients immobilized with CIVCO's Kneefix and Feetfix. We found that the usually applied isotropic setup margin of 8mm covered all the uncertainties related to patient setup for most RT treatments of the pelvis. However, margins of even 10.3mm were needed for the female patients with very large pelvic target volumes centered either in the symphysis or in the sacrum containing both of these structures. This was because the effect of rotation (p ≤ 0.02) and the observer variation in image matching (p ≤ 0.04) were significantly larger for the female patients than for the male patients. Even with daily image guidance, the required margins remained larger for the women. Patient rotations were largest about the lateral axes. The difference between the required margins was only 1mm for the 2 immobilization devices. The largest component of overall systematic position error came from patient rotation. This emphasizes the need for rotation correction. Overall, larger position errors and setup margins were observed for the female patients with pelvic cancer than for the male patients.
Medical dosimetry : official journal of the American Association of Medical Dosimetrists.Med Dosim.2014 Spring;39(1):74-8. doi: 10.1016/j.meddos.2013.09.009. Epub 2014 Jan 3.
We evaluated adequate setup margins for the radiotherapy (RT) of pelvic tumors based on overall position errors of bony landmarks. We also estimated the difference in setup accuracy between the male and female patients. Finally, we compared the patient rotation for 2 immobilization devices. The stud
PMID 24393499

A refined method for multivariate meta-analysis and meta-regression.

Jackson D, Riley RD.Author information MRC Biostatistics Unit, Institute of Public Health, Cambridge, U.K.AbstractMaking inferences about the average treatment effect using the random effects model for meta-analysis is problematic in the common situation where there is a small number of studies. This is because estimates of the between-study variance are not precise enough to accurately apply the conventional methods for testing and deriving a confidence interval for the average effect. We have found that a refined method for univariate meta-analysis, which applies a scaling factor to the estimated effects' standard error, provides more accurate inference. We explain how to extend this method to the multivariate scenario and show that our proposal for refined multivariate meta-analysis and meta-regression can provide more accurate inferences than the more conventional approach. We explain how our proposed approach can be implemented using standard output from multivariate meta-analysis software packages and apply our methodology to two real examples. Copyright © 2013 John Wiley & Sons, Ltd.
Statistics in medicine.Stat Med.2014 Feb 20;33(4):541-54. doi: 10.1002/sim.5957. Epub 2013 Aug 29.
Making inferences about the average treatment effect using the random effects model for meta-analysis is problematic in the common situation where there is a small number of studies. This is because estimates of the between-study variance are not precise enough to accurately apply the conventional m
PMID 23996351

Thermal inactivation kinetic modeling of human norovirus surrogates in blue mussel (Mytilus edulis) homogenate.

Bozkurt H1, Leiser S2, Davidson PM1, D'Souza DH3.Author information 1Department of Food Science and Technology, The University of Tennessee, 2600 River Drive, Knoxville, TN 37996-4591, USA.2Institute of Food Science and Biotechnology, University of Hohenheim, Garbenstraße 25, 70599 Stuttgart, Germany.3Department of Food Science and Technology, The University of Tennessee, 2600 River Drive, Knoxville, TN 37996-4591, USA. Electronic address: ddsouza@utk.edu.AbstractControl of seafood-associated norovirus outbreaks has become an important priority for public health authorities. Due to the absence of human norovirus infectivity assays, cultivable surrogates such as feline calicivirus (FCV-F9) and murine norovirus (MNV-1) have been used to begin to understand their thermal inactivation behavior. In this study, the effect of thermal treatment on inactivation of human norovirus surrogates in blue mussels was investigated at 50, 56, 60, 65, and 72°C for various times (0-6min). The results obtained were analyzed using the Weibull and first-order models. The Theil error splitting method was used for model comparison. This method splits the error in the predicted data into fixed and random error. This method was applied to select satisfactory models for determination of thermal inactivation of norovirus surrogates and kinetic modeling. The D-values calculated from the first-order model (50-72°C) were in the range of 0.07 to 5.20min for FCV-F9 and 0.18 to 20.19min for MNV-1. Using the Weibull model, the tD=1 for FCV-F9 and MNV-1 to destroy 1log (D=1) at the same temperatures were in the range of 0.08 to 4.03min and 0.15 to 19.80min, respectively. The z-values determined for MNV-1 were 9.91±0.71°C (R(2)=0.95) using the Weibull model and 11.62±0.59°C (R(2)=0.93) for the first-order model. For FCV-F9 the z-values were 12.38±0.68°C (R(2)=0.94) and 11.39±0.41°C (R(2)=0.97) for the Weibull and first-order models, respectively. The Theil method revealed that the Weibull model was satisfactory to represent thermal inactivation data of norovirus surrogates and that the model chosen for calculation of thermal inactivation parameters is important. Knowledge of the thermal inactivation kinetics of norovirus surrogates will allow development of processes that produce safer shellfish products and improve consumer safety.
International journal of food microbiology.Int J Food Microbiol.2014 Feb 17;172:130-6. doi: 10.1016/j.ijfoodmicro.2013.11.026. Epub 2013 Dec 4.
Control of seafood-associated norovirus outbreaks has become an important priority for public health authorities. Due to the absence of human norovirus infectivity assays, cultivable surrogates such as feline calicivirus (FCV-F9) and murine norovirus (MNV-1) have been used to begin to understand the
PMID 24412376

Japanese Journal

格子条件下でのランダム符号化誤り確率の漸近展開について (情報理論)

本多淳也
電子情報通信学会技術研究報告 = IEICE technical report : 信学技報 114(438), 41-46, 2015-01-30
NAID 40020364386

Cコンパイラの算術最適化を対象としたテストスイートCF3

日比野佑亮,石浦菜岐佐
情報処理学会研究報告. SLDM, [システムLSI設計技術] 2015-SLDM-169(21), 1-6, 2015-01-22
本稿では,C コンパイラの算術最適化,特に定数畳み込みを対象としたテストスイート CF3 を提案する.C コンパイラ用ランダムテスト Orange3 は,GCC や LLVM/Clang の最新版の不具合を検出する強力なテストシステムだが,コンパイラによっては同じ不具合を検出するエラープログラムが多数生成されるため,不具合の特定が効率的に行えないことがある.本稿では,Orange3 が GCC の …
NAID 110009868153

McNabb-Foster式により再現したTDS放出曲線のガウス分布によるピーク分離

土田豊
圧力技術 53(2), 96-101, 2015
… This peak corresponding to interstitial hydrogen can be understood by random walk model where hydrogen atoms jump between interstitial sites to trap sites randomly. … Distribution of hydrogen trapped by 150°C (423K) peak in the case (b) was slightly different from Gaussian distribution through the effect of 280°C (553K) trap, but it would not matter, considering the possible error in TDS measurement. …
NAID 130005068058