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Given two measurements $\overline{x}_1$ and $\overline{x}_2$ with standard uncertainty $u_i$. The measurement uncertainty states that with a probability of $\approx 68\%$ the conventional true value of the measurand is inside the confidence interval: $$\overline{x}_i \pm u_i$$

How to answer whether both measurements $\overline{x}_1$ and $\overline{x}_2$ target the same measurand, i.e., they measured the same quantity?

EDIT 1: By uncertainty, I mean a standard uncertainty, e.g., obtained by following the GUM and use a Type B evaluation. Moreover, I am not interested in a new estimate from both measurements.

EDIT 2: Am I thinking wrong, or is the question wrongly stated? Or is the question only to be answered if the sample size/number of indications of both measurements is known?

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  • $\begingroup$ Could you explain what the "sample size" of a measurement might be? And could you clarify what you mean by "statistical significance between them that they do not both contain the same best estimate of the same measurand"? This could be interpreted in several ways, such as whether they measure the same quantity or whether neither is close to whatever they are measuring. $\endgroup$ – whuber Feb 23 at 15:01
  • $\begingroup$ I edited and precise the question hopefully. $\endgroup$ – kenomo Feb 23 at 15:53
  • $\begingroup$ Do you want your new estimate of $\mu$ to use both $\bar X_1$ and $\bar X_2?$ If so, it is necessary to know the sizes $n_1$ and $n_2$ of the two samples. Also need to know what you mean by 'uncertainty $u_i:$ there are various ways to quantify uncertainty. $\endgroup$ – BruceET Feb 23 at 16:47
  • $\begingroup$ By uncertainty, I mean a standard uncertainty, e.g., obtained by following the GUM and use a Type B evaluation. I am not interested in a new estimate from both measurements. $\endgroup$ – kenomo Feb 23 at 17:00