- #1
How Is the Variance Used as Weight in Half-Life Error Analysis?
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Homework Help Overview
The discussion revolves around the concept of error analysis in the context of half-life determination, specifically focusing on the role of variance as a weight in fitting data. Participants are exploring the implications of a constant background in measurements and how it affects the analysis of half-life without relying solely on fitting methods.
Discussion Character
- Exploratory, Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants are questioning the meaning of "constant background" and its implications for deducing half-life. There are inquiries about the relationship between statistical error and standard error, as well as the underlying distribution related to the data. Some are attempting to connect the Poisson distribution to the concept of variance as a weight in fitting.
Discussion Status
The discussion is active, with participants raising foundational questions and exploring various interpretations of error analysis concepts. Some guidance has been provided regarding the statistical properties of distributions, but there is no explicit consensus on the terminology or its application in the context of the problem.
Contextual Notes
Participants note a lack of specific references to "constant background" in their resources, which may affect their understanding. There is also mention of the absence of equations in the original problem statement, which could limit the depth of analysis.
- #2
Mark44
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Does the textbook or other resource talk about the term "constant background"? Does it give any examples of what they're talking about?schniefen said:
- #3
schniefen
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It has the following section:
How is the statistical error related to the standard error? Are they the same? I have not read a lot of error analysis, although this is probably a very basic question. I'm familiar with estimators and the like, and probability theory in general. "Constant background" is not mentioned.
How is the statistical error related to the standard error? Are they the same? I have not read a lot of error analysis, although this is probably a very basic question. I'm familiar with estimators and the like, and probability theory in general. "Constant background" is not mentioned.
- #4
Mark44
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From wikipedia ( https://en.wikipedia.org/wiki/Standard_error )
What's the underlying distribution here? In a normal distribution the parameters are the mean (##\mu##) and standard deviation (\sigma). In this kind of distribution, the parameters are related, as they seem to be in the text you quoted.
From that text, it appears that they are assuming a Poisson distribution, in which the mean (##\mu##) and variance (##\sigma^2##) are equal. So ##\mu = \lambda = \sigma^2##, or ##\sigma = \sqrt{\lambda}##. In the text, ##\lambda = N##.
I don't understand their terminology of "the value from the fit as the weight."
The standard error of the mean is ##\sigma_x = \frac {\sigma}{\sqrt n}##
What's the underlying distribution here? In a normal distribution the parameters are the mean (##\mu##) and standard deviation (\sigma). In this kind of distribution, the parameters are related, as they seem to be in the text you quoted.
From that text, it appears that they are assuming a Poisson distribution, in which the mean (##\mu##) and variance (##\sigma^2##) are equal. So ##\mu = \lambda = \sigma^2##, or ##\sigma = \sqrt{\lambda}##. In the text, ##\lambda = N##.
I don't understand their terminology of "the value from the fit as the weight."
- #5
schniefen
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It must be the Poisson distribution as you say, since "number of counts in one channel" most likely refers to some kind of decay.
How does one use the variance ##\sigma^2=N## as the "weight in a fit"?
How does one use the variance ##\sigma^2=N## as the "weight in a fit"?
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