Chiro is a very diplomatic and patient person and hasn't criticized your writing and vocabulary - but I will.
What do you mean by "measurements agree to within 1 part in 50 with theory"? You haven't clearly described the problem. One guess is that you have some determinisitic theoretical formula y = f(x). You have taken several different value of the control variable x, say x0, x1,.. and for each value, you have measured several different values of y. So, for example, for x= x1, you have a set of measurements y11, y12, y13,.... If that is the case there are two things involved in a "disagreement" with theory. A given y value can differ from the predicted y value and, for given size difference, a certain number of the measurements can produce that difference or smaller. What are you asking about? Is this a question about analyzing the set of y's for an individual value of x as a separate problem? Or are you asking about how to test some hypothesis about entire set of data?
It is advisable when discussing situations involving probability, to simply use the word "probability" to refer to probability instead of a variety of other words (such as "chance", "uncertainty", "confidence"). In particular, a "confidence level" has a technical meaning in statistics. It's a term used in the theory of estimation. What meaning do you wish to convey by the term "confidence level"?