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Accuracy of Numerical Measurements and Analyses: Random and Systematic Errors

Accuracy of Numerical Measurements and Analyses: Random and Systematic Errors

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Accuracy: Random and Systematic Errors Accuracy: Random and Systematic Errors Presentation Transcript

  • Accuracy of Numerical Results Random and Systematic Errors October 2010
    • Introduction
    • Random Errors
    • Systematic Errors
    • Propagation of Errors
    Accuracy of Numerical Results
  • Introduction
    • Numerical results or analyses are an integral aspect of most research papers.
    • To ensure accuracy , and therefore reliability and integrity of the results:
    • Take into account experimental conditions or the method of data collection
    • Determine sources of error (random or systematic)
    • Errors are inherent to all data, and are distinct from mistakes or blunders !!
    • Examine and include contribution to errors from all sources
    • Assign appropriate errors to measured or derived quantities
    • Introduction
    • Random Errors
    • Systematic Errors
    • Propagation of Errors
    Accuracy of Numerical Results
  • Random Errors - I
    • Simultaneous measurements of the same quantity: values distributed accordingly to the probability of occurrence (probability distribution)
    • Sources of random errors
      • Statistical effects
      • Limitations in the measurement process
    • Common probability distributions
    • Different forms of binomial distribution (low probability of occurrence/success)
      • Small number of measurements or sample size ( Poisson )
      • Large number of measurements or sample size ( Gaussian )
  • Random Errors - II
    • The distributions associated with the broad categories of random errors are:
    • Poisson distribution
      • Small sample size
      • Discrete and asymmetric
    • Gaussian/normal distribution
      • Large sample size
      • Continuous and symmetric
    -> Value Probability density -> Mean A typical Gaussian distribution indicating the probability of occurrence for a given value. μ indicates the mean value, while σ denotes the standard deviation. For an ideal Gaussian, 68.2% of the values would lie between 1 σ of the mean value , 95.4% between 2 σ , and 99.7% between 3 σ , as indicated in the above figure.
    • Introduction
    • Random Errors
    • Systematic Errors
    • Propagation of Errors
    Accuracy of Numerical Results
  • Systematic Errors - I
    • Systematic errors tend to bias measured values in a pre-determined manner
    • Possible sources of systematic errors
      • Imperfections in the measuring equipment
      • Incorrect use of apparatus or implementation of techniques
    • Isolating/reducing systematic errors
      • Examine and analyze measurement apparatus and techniques
      • Careful practices in the implementation of research
  • Systematic Errors - II
    • Similar experiments performed at
    • different laboratories with varying
    • conditions and equipment have
    • unique associated systematic errors
    • If two different experiments report
    • results about the same quantity
    • which are variance with each
    • other, this may be due to incorrect
    • or incomplete treatment of
    • systematic errors in one or both.
    Systematic errors lead to a difference in the actual and measured values. In this simple example, the error can be characterized in terms of a difference in the offset (values at zero) and slope of the two lines.
    • Introduction
    • Random Errors
    • Systematic Errors
    • Propagation of Errors
    Accuracy of Numerical Results
  • Propagation of Errors
    • Isolate and quantify all sources of random and systematic errors
    • Combine all sources of error: cumulative error on the measured quantity
    • Different procedure based on whether measured quantities are dependent or independent of each other
    • Reliability of quoted values depends on rigorous and thorough error analysis
    • Accurate values , with appropriate error bars , ensure sound results , which are respected by peers
  • About Crimson
    • Enago ™ is the leading editing and publication service provider for scientific
    • manuscripts in Japan, and has a total of over 10000 clients in many countries.
    • Ulatus™ provides Japanese to English translation services in numerous
    • subject areas for almost every document type.
    • Voxtab™ is the transcription arm of our business and provides accurate and
    • reliable transcriptions, with fast turnaround times.
    英文编辑 · 英文校对 http:// www.enago.cn / 英文編修‧論文修改 http:// www.enago.tw / 英語テープ起こしボックスブ http:// www.voxtab.jp / 日英・英日翻訳ユレイタス http:// www.ulatus.jp / 英文校正エナゴ http:// www.enago.jp / English Transcription Services http:// www.voxtab.com / English Translation Services http:// www.ulatus.com / English Editing Services http:// www.enago.com /