Measurement Error Analysis in Gaussian distribution

  • #1
Govind
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TL;DR Summary
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

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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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  • #2
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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  • #3
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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What is measurement error analysis in Gaussian distribution?

Measurement error analysis in Gaussian distribution is a statistical method used to quantify and analyze the errors or uncertainties in measurements that follow a Gaussian or normal distribution. It involves identifying and evaluating the sources of error and their impact on the final measurement result.

What is a Gaussian distribution?

A Gaussian distribution, also known as a normal distribution, is a probability distribution that is symmetrical and bell-shaped. It is characterized by its mean and standard deviation, which determine the shape and spread of the distribution. Many natural phenomena and measurements in science follow a Gaussian distribution.

What are the sources of measurement errors in Gaussian distribution?

The sources of measurement errors in Gaussian distribution can be classified into two types: systematic errors and random errors. Systematic errors are consistent and repeatable errors caused by flaws in the measurement process, while random errors are unpredictable and occur due to chance factors.

How are measurement errors quantified in Gaussian distribution?

Measurement errors in Gaussian distribution are quantified using statistical measures such as mean, standard deviation, and variance. These measures provide information about the central tendency and spread of the data, which can then be used to estimate the magnitude of the errors.

Why is measurement error analysis important in Gaussian distribution?

Measurement error analysis in Gaussian distribution is important because it allows scientists to assess the reliability and accuracy of their measurements. By understanding and quantifying the errors, scientists can improve their measurement techniques and make more informed conclusions based on their data.

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