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What Level Of Statistical Fluctuations Do I Expect

We've put together a study in order to assess the scale of statistical fluctuations we expect from using 10,000 generated events for every tag. This study is located in docdb 13265. The main points you should remember are that:

  • The example plots shown on this page are an updated version of the plots found in docdb 13265 which compares two statistically independent sets of 10,000 generated events, which were both generated from the same tag. That means that these plots show as close to "perfect" agreement as we can expect within statistical fluctuations).
  • These comparisons are area normalised, meaning that a single high bin can make agreement look worse than it is.

Hit Plots
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hit_channel_plane0/1/2

The hits per plane plots are particularly tricky:

Plane0 (the first induction plane):

Plane1 (the second induction plane):

Plane2 (the collection plane)

There appear to be no error bars, but this is because there are a huge number of hits in every event, meaning the fractional statistical uncertainty is very small. This is further complicated by the fact that the hits are (for the most part) correlated with the track positions, which have much higher statistical uncertainties, meaning that the level of statistical fluctuations on the Y plane are expected, even though the error bands are very small.

hit_charge

hit_multiplicity

no_hits

Bins with low statistics can have larger levels of disagreement, as shown below:

We're really interested in the overall shape agreement.

Track Plots
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ntracks

trkphi

As noted above, with 10k events, rconstructed tracks and showers are expected to have much larger statistical variations than hits, meaning something like this trk_phi distribution is considered normal.

trktheta

Shower Plots
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nshowers

shwr_phi

shwr_theta

Calorimetry Plots
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trkdqdx_plane0

trkdqdx_plane1

trkdqdx_plane2

Flash Plots
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flsPe_simpleFlashBeam

flsPe_simpleFlashCosmic

flsTime_simpleFlashBeam

NOTE: THIS DISTRIBTUION WAS PRODUCED WITH AN IN-TIME SAMPLE RATHER THAN AN OPEN COSMIC SAMPLE, MEANING THE SHAPE OF THE DISTRIBUTION IS VERY DIFFERENT FROM WHAT IS OBSERVED IN THE CI VALIDATION.

flsTime_simpleFlashCosmic

NOTE: THIS DISTRIBTUION WAS PRODUCED WITH AN IN-TIME SAMPLE RATHER THAN AN OPEN COSMIC SAMPLE, MEANING THE SHAPE OF THE DISTRIBUTION IS VERY DIFFERENT FROM WHAT IS OBSERVED IN THE CI VALIDATION.

nfls_simpleFlashBeam

NOTE: THIS DISTRIBTUION WAS PRODUCED WITH AN IN-TIME SAMPLE RATHER THAN AN OPEN COSMIC SAMPLE, MEANING THE SHAPE OF THE DISTRIBUTION IS VERY DIFFERENT FROM WHAT IS OBSERVED IN THE CI VALIDATION.

nfls_simpleFlashCosmic