Since error bars are typically +-1 sigma, you expect about 1/3 of all measurements to be further away from the true value than the error bar, if all error estim

Since error bars are typically +-1 sigma, you expect about 1/3 of all measurements to be further away from the true value than the error bar, if all error estimates are correct, and uncorrelated. That's actually a check a lot of doctored data fails.