Summary

An analysis of the crate variations results in a crate systematic of 0.9%. This increases the total calibration uncertainty to 1.6%.

Detailed Explanation:

If we look at the distribution of E/p for each crate, there seems to be a non-statistical fluctuation variation in the values. We suspect the cause of these fluctuations is the timing.

Figure 1: Crate fits y: E/p, x: crate

To quantify the uncertainty that this variation brings into the I took the electrons and partitioned them into 30 random groups. I then fit then found the mean E/p for these 30 random groups and the RMS about that mean. I then repeated the partitioning 4 more times and calculated the RMS about the first mean.

Here are the RMSes and the uncertainties for those 5 different random partitions about the same mean:

0.0153604 0.00289072
0.0157013 0.00268148
0.0146855 0.00271402
0.0153595 0.0027823
0.012489 0.0027293

Figure 2: Random Fit:

Now if I calculate the RMS using all 30 crates, I get a value ~ twice those of the randoms with a 50% uncertainty. However, if I remove the outlier (crate 12), then I get the following numbers:
0.0163393 0.00270009

These indicate that the single outlier is the source of the deviation, so the crate systematic will be an estimate of this crate's contribution to the total uncertainty. Each crate contributes roughly 1/15 of the statistics for each of 20 eta rings. Thus, an estimate of the uncertainty is the deviation of this crate from the mean divided by 15. This value works out to be 0.9% which adds in quadrature for the previous value of 1.3%. This brings the total uncertainty to 1.6%

Figure 3: Crate 12: