Measurement Error Analysis in Gaussian distribution

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SUMMARY

This discussion focuses on the concepts of measurement error analysis within the context of Gaussian distribution, specifically addressing ISO guidelines for Accuracy, Precision, Uncertainty, and Error. Participants clarify that when systematic error is zero, the average of measurements can equal the true value, despite the presence of random errors. The conversation emphasizes the distinction between population averages and finite sample averages, and the need for a comprehensive graph that illustrates all relevant measurement parameters, including Random Error, Systematic Error, Total Error, Uncertainty, Accuracy, Precision, and Trueness.

PREREQUISITES
  • Understanding of Gaussian distribution and its properties
  • Familiarity with ISO guidelines for Accuracy and Precision
  • Knowledge of statistical concepts such as Random Error and Systematic Error
  • Basic graph interpretation skills in the context of probability distributions
NEXT STEPS
  • Research the ISO 5725 standard for Accuracy and Precision in measurements
  • Learn about the Central Limit Theorem and its implications for sample averages
  • Explore techniques for visualizing measurement errors in statistical graphs
  • Study the differences between Total Error and Uncertainty in measurement contexts
USEFUL FOR

Statisticians, quality control professionals, researchers in measurement science, and anyone interested in understanding the intricacies of measurement error analysis in Gaussian distributions.

Govind
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TL;DR
Could someone post a single graph ( adding some more details in first graph about accuracy precision and Trueness) of probability distribution in which all the parameters of measurement like Random error, Systematic error, Total error, Uncertainity, Accuracy, Precision and Trueness are described? It would also be fine if you upload a photo a hand-drawn graph in copy rather than a printed one.
I am new to statistics and recently learned about ISO guidelines for Accuracy & Precision and Uncertainty & Error. But there are some graphs of probability distribution I found on internet which I am not able to grasp.

2wXfN.png

image Source

Q. In this graph(above) if systematic error is zero then average value will be the true value! How's that possible? i.e. if we take measurements under a condition of zero systematic error , average of whatever we measured will be equal to true value but aren't there some random error in average of measurement? And why random error here is described with respect to measured value not to mean of measured value?

jA3bT.png


Image Source

In first graph total and random errors are described wrt measured value not to mean of measurements and here in 2nd graph accuracy and precision are related to mean of measurement, no concept of measured value.
Could someone post a single graph ( adding some more details in first graph about accuracy precision and Trueness) of probability distribution in which all the parameters of measurement like Random error, Systematic error, Total error, Uncertainity, Accuracy, Precision and Trueness are described? It would also be fine if you upload a photo a hand-drawn graph in copy rather than a printed one.
 
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I will not make a graph that tries to answer all possible questions that you may have, but I am willing to try to answer specific questions.
The "average" that you are talking about in the graph is the population average of the distribution -- the distribution mean. That is as though you had the average of an infinite sample. Any finite sample that you take an average of will not give you the exact average shown in the graph.
 
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FactChecker said:
I will not make a graph that tries to answer all possible questions that you may have, but I am willing to try to answer specific questions.
The "average" that you are talking about in the graph is the population average of the distribution -- the distribution mean. That is as though you had the average of an infinite sample. Any finite sample that you take an average of will not give you the exact average shown in the graph.
Is this graph(below) I have made correct according to ISO definations? ( links of definations are provided in question)

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