1. 1 Practical Statistics for Physicists SLUO Lectures February 2007 Louis Lyons Oxford l.lyons@physics.ox.ac.uk

2. 2 Topics 1) Introduction Learning to love the Error Matrix 2) Do’s and Dont’s with L ikelihoods 3) χ 2 and Goodness of Fit 4) Discovery and p-values

3. 3 Books Statistics for Nuclear and Particle Physicists Cambridge University Press, 1986 Available from CUP Errata in these lectures

4. 4 Other Books CDF Statistics Committee BaBar Statistics Working Group

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10 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 CONTRAST Total = 198 ± 10 K GENERAL POINT: Adding (uncontroversial) theoretical input can improve precision of answer Compare “kinematic fitting”

11. 11

12. 12 Relation between Poisson and Binomial PeopleMaleFemale PatientsCuredRemain ill Decaying nuclei ForwardsBackwards Cosmic raysProtonsOther particles N people in lecture, m males and f females (N = m + f ) Assume these are representative of basic rates : ν people νp males ν(1-p) females Probability of observing N people = P Poisson = e –ν ν N /N! Prob of given male/female division = P Binom = p m (1-p) f Prob of N people, m male and f female = P Poisson P Binom = e –νp ν m p m * e -ν(1-p) ν f (1-p) f m! f ! = Poisson prob for males * Poisson prob for females

13. 13

14. 14 Relevant for Goodness of Fit

15. 15

16. 16

17. 17

18. 18 Gaussian = N (r, 0, 1) Breit Wigner = 1/{π * (r 2 + 1)}

19. 19 Learning to love the Error Matrix Introduction via 2-D Gaussian Understanding covariance Using the error matrix Combining correlated measurements Estimating the error matrix

20. 20 Element E ij - Diagonal E ij = variances Off-diagonal E ij = covariances

21. 21

22. 22

23. 23

24. 24

25. 25

26. 26

27. 27

28. 28

29. 29

30. 30

31. 31

32. 32 Small error Example: Lecture 3 x best outside x 1  x 2 y best outside y 1  y 2

33. 33

34. 34

35. 35

36. 36 Conclusion Error matrix formalism makes life easy when correlations are relevant

37. 37 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