# Quantify significance between measured value and prediction (with error)?

I have a question about the proper way to describe the results I get to a prediction (both of which have statistical errors). I get a result with 1-sigma, let's say:

-1 +/- 2


There is a published prediction (and 1-sigma error) for this measured value, let's say:

4 +/- 1.5.


If there is a precise way of describing my result? I mean, should I say, "this is consistent within 2-sigma?" or "it's inconsistent... sorta"?

I would like to be able to quantify the significance of the disagreement (or agreement) between the measurement and the prediction.

If it's easier to use variables instead of numbers, let's use my result is a +/- b; predicted value: x +/- y.

## 1 Answer

I've decided what I'm going to do with this problem -- if you have a more clever idea, please let me know.

Add the two statistical errors in quadrature and quantify the difference between them in units of that new, larger error.

Measured: a +/- b
predicted value: x +/- y

total_sigma = sqrt(b^2 + y^2)


Deviations away ~ abs(x - a) / total_sigma.