Practical Statistics for Physicists
Louis Lyons
Oxford
l.lyons@physics.ox.ac.uk
SLUO Lectures
February 2007
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Topics
1) Introduction
Learning to love the Error Matrix
2) Do’s and Dont’s with Likelihoods
3) χ2 and Goodness of Fit
4) Discovery and p-values
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Books
Statistics for Nuclear and Particle Physicists
Cambridge University Press, 1986
Available from CUP
Errata in these lectures
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Other Books
CDF Statistics Committee
BaBar Statistics Working Group
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Difference between averaging and adding
Isolated island with conservative inhabitants
How many married people ?
Number of married men
= 100 ± 5 K
Number of married women = 80 ± 30 K
Total = 180 ± 30 K
Weighted average = 99 ± 5 K
Total = 198 ± 10 K
CONTRAST
GENERAL POINT: Adding (uncontroversial) theoretical input can
improve precision of answer
Compare “kinematic fitting”
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Relation between Poisson and Binomial
N people in lecture,
m males
and
f females
(N = m + f )
Assume these are representative of basic rates: ν people
Prob of given male/female division = PBinom =
=
e–νp νm pm
*
m!
ν(1-p) females
= e–ν ν N /N!
Probability of observing N people = PPoisson
Prob of N people, m male and f female =
νp males
N! m
p
m! f !
(1-p)f
PPoisson PBinom
e-ν(1-p) νf (1-p)f
f!
= Poisson prob for males * Poisson prob for females
People
Male
Female
Patients
Cured
Remain ill
Decaying
nuclei
Forwards
Backwards
Cosmic rays
Protons
Other particles
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Relevant for Goodness of Fit
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Gaussian = N (r, 0, 1)
Breit Wigner = 1/{π * (r2 + 1)}
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Learning to love the Error Matrix
• Introduction via 2-D Gaussian
• Understanding covariance
• Using the error matrix
Combining correlated measurements
• Estimating the error matrix
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Element Eij - <(xi – xi) (xj – xj)>
Diagonal Eij = variances
Off-diagonal Eij = covariances
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Small error
Example: Lecture 3
xbest outside x1  x2
ybest outside y1  y2
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Conclusion
Error matrix formalism makes
life easy when correlations are
relevant
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Next time: Likelihoods
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What it is
How it works: Resonance
Error estimates
Detailed example: Lifetime
Several Parameters
Extended maximum L
• Do’s and Dont’s with L
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