If a particular experiment is done to determine a particular value, say the charge radius of a particle, and they give a 'sigma' of two and a 'margin of error' of a femtometer, does that mean there is a 95% chance of the particle's true radius laying within a femtometer of the given number?
An example from Scientific American:
PHYSICS Missing Neutrons May Lead a Secret Life as Dark Matter. This may be the reason experiments can’t agree on the neutron lifetime, according to a new idea.
By Clara Moskowitz on January 29, 2018
Both classes of experiments find neutrons can last for only about 15 minutes outside of atoms. But bottle experiments measure an average of 879.6 seconds plus or minus 0.6 second, according to the Particle Data Group, an international statistics-keeping collaboration. Beam experiments get a value of 888.0 seconds plus or minus 2.0 seconds. The 8.4-second difference may not seem like much, but it is larger than either of the calculations’ margins of error—which are based on the experimenters’ understanding of all the sources of uncertainty in their measurements. The difference leaves the two figures with a statistically significant “4-sigma” deviation. Experimenters behind both methods have scoured their setups for overlooked problems and sources of uncertainty, with no luck so far.