2
PARADOXHistogram with 100 binsFit 1 parameter
Smin: χ2 with NDF = 99 (Expected χ2 = 99 ± 14)
For our data, Smin(p0) = 90
Is p1 acceptable if S(p1) = 115?
1) YES. Very acceptable χ2 probability
2) NO. σp from S(p0 +σp) = Smin +1 = 91
But S(p1) – S(p0) = 25
So p1 is 5σ away from best value
9
Learning to love the Error Matrix
• Resume of 1-D Gaussian• Extend to 2-D Gaussian• Understanding covariance• Using the error matrix Combining correlated measurements• Estimating the error matrix
24
Difference between averaging and adding
Isolated island with conservative inhabitantsHow many married people ?
Number of married men = 100 ± 5 KNumber of married women = 80 ± 30 K
Total = 180 ± 30 KWeighted average = 99 ± 5 K CONTRAST Total = 198 ± 10 K
GENERAL POINT: Adding (uncontroversial) theoretical input can improve precision of answer
Compare “kinematic fitting”
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