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

[CCofADoa]

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.

 

[mjc123]

It's a bit more complicated when the measurements have different standard errors. Suppose independent measurements x and y are Normally distributed, with means μ_x and μ_y, and variances σ_x² and σ_y². (We use variance rather than standard deviation because variances are additive). The difference x-y is Normal with mean μ_x - μ_y, and variance σ_x² + σ_y². The t-value is then
t = (x - y)/√(σ_x² + σ_y²)

 

[CCofADoa]

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.