A Pause for Reflection — Question 10

Question 10

A model prediction needs an uncertainty before its residual can be judged

A supplied model predicts R=.250 with independent theoretical uncertainty .010. An experiment measures R=.278 with statistical uncertainty .006 and systematic uncertainty .008, all treated as Gaussian.

1. Combine the experimental errors and calculate the model-data pull.

2. If statistical uncertainty falls by a factor of three, recompute the pull and explain the limited improvement.

Question 10 - Solution

A model prediction needs an uncertainty before its residual can be judged

(a) Method and calculation

$$\boxed{\sigma_{\mathrm{exp}}=\sqrt{.006^2+.008^2}=.010}.$$$$\boxed{z=.028/\sqrt{.010^2+.010^2}=1.97990}.$$

(b) Interpretation and further calculation

$$\sigma_{\mathrm{exp,new}}=\sqrt{.002^2+.008^2}=.00824621.$$$$\boxed{z_{\mathrm{new}}=.028/\sqrt{.010^2+.008^2+.002^2}=2.16025}.$$

Physical check

More events reduce statistical error but not the stated theory and systematic terms. Correlations would require a covariance calculation.