When are measurements in agreement with a theory?

Of course, we never expect exact fit: there are always instrument imperfections, environmental influences that could not be fully screened out, and so on. (In fact, an exact fit is a sign of fudged results.) What we expect is thjat the measurements are "close enough."

But how close is that? Here is Thomas Kuehn's finding:

"I now conclude that the only possible criterion is the mere fact that [the measurements] appear, together with the theory from which they are derived, in a professionally accepted text." -- "The Function of Measurement in Modern Physical Science"