I need to determine if two quantities, A and 𝐵, with their associated uncertainties, $u_A$ and $u_B$, are statistically different.
Both quantities have been derived from measurements. The uncertainties were calculated using uncertainty propagation. One conservative approach I know of is comparing the difference using:
$|A-B| > 1.96 \sqrt{(u_A^2 + u_B^2)}$
This provides a threshold for determining a significant difference at a 95% confidence level.
However, I’m looking for a less conservative approach that can:
- Test the difference between the two values considering their uncertainties.
- Provide a p-value to quantify the statistical significance.
What would be the best statistical method for this, and how would it account for the uncertainties associated with each value?
Thank you!
