1. 1 Practical Statistics for Physicists Dresden March 2010 Louis Lyons Imperial College and Oxford CDF experiment at FNAL CMS expt at LHC l.lyons@physics.ox.ac.uk

2. 2 Topics 1) Learning to love the Error Matrix 2) Do’s and Dont’s with L ikelihoods 3) Discovery and p-values

3. 3 Some of the questions to be addressed What is coverage, and do we really need it? Should we insist on at least a 5σ effect to claim discovery? How should p-values be combined? If two different models both have respectable χ 2 probabilities, can we reject one in favour of other? Are there different possibilities for quoting the sensitivity of a search? How do upper limits change as the number of observed events becomes smaller than the predicted background? Combine 1 ± 10 and 3 ± 10 to obtain a result of 6 ± 1? What is the Punzi effect and how can it be understood?

4. 4 Books Statistics for Nuclear and Particle Physicists Cambridge University Press, 1986 Available from CUP Errata in these lectures

5. 5 Other Books CDF Statistics Committee BaBar Statistics Working Group

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7. 7 Learning to love the Error Matrix Introduction via 2-D Gaussian Understanding covariance Using the error matrix Combining correlated measurements Estimating the error matrix

8. 8 Gaussian or Normal

9. 9 0.002

10. 10 Relevant for Goodness of Fit

11. 11 Correlations Basic issue: For 1 parameter, quote value and error For 2 (or more) parameters, (e.g. gradient and intercept of straight line fit) quote values + errors + correlations Just as the concept of variance for single variable is more general than Gaussian distribution, so correlation in more variables does not require multi-dim Gaussian But more simple to introduce concept this way

12. 12 a b x y

13. 13 Element E ij - Diagonal E ij = variances Off-diagonal E ij = covariances

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25. 25 Small error Example: Chi-sq Lecture x best outside x 1  x 2 y best outside y 1  y 2

26. 26 a b x y

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30. 30 Conclusion Error matrix formalism makes life easy when correlations are relevant

31. 31 Next time: L ikelihoods What it is How it works: Resonance Error estimates Detailed example: Lifetime Several Parameters Extended maximum L Do’s and Dont’s with L 