How to compare two measurements with uncertainties in terms of sigma?

AI Thread Summary
The discussion focuses on comparing two measurements with uncertainties using the t-value. It explains how to calculate the t-value and determine if a measured value is within one sigma of another. The conversation raises questions about whether to consider the uncertainties of the reference value and the terminology used in different regions regarding sigma comparisons. Additionally, it highlights the complexity of handling measurements with different standard errors and the need for clearer references on error propagation in various contexts. The thread emphasizes the challenges in finding comprehensive resources on these statistical concepts.
CCofADoa
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Homework Statement
For example, we measured some quantity in our lab 1.0 +/- 0.1 GeV, but another lab measured 0.98 +/- 0.01 GeV. How can we say something like, "Our measurement is within 2 sigma of the other measurement or reference value"? Does that kind statement event make sense?
Relevant Equations
There was something called t-value, which is defined by:

t = (measured value - accepted value) / standard error of measured value
Perhaps that statement is just saying how big the t-value is.

Like, in this case:

t = (1.0 - 0.98) / 0.1 = 0.1

So we can say that our measured value is within 1 sigma from the other measured value.
In this case, do we just ignore the uncertainties of the other measured/reference value?

It's possible this is a language problem, and you just don't say this in English. Because I was not able to find anything from googling about it.
 
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It's a bit more complicated when the measurements have different standard errors. Suppose independent measurements x and y are Normally distributed, with means μx and μy, and variances σx2 and σy2. (We use variance rather than standard deviation because variances are additive). The difference x-y is Normal with mean μx - μy, and variance σx2 + σy2. The t-value is then
t = (x - y)/√(σx2 + σy2)
 
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Thanks a lot.

So, do people even say, "Our result is within 1 sigma from the accepted value" when they are talking about the t-value? Perhaps it's just the people in my country.

Personally I always find it difficult to find the references for this stuff, beyond basic error propagation. For example, how error propagation works in a curve fitting, or in a matrix inversion, etc.
 
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