The Benefit of Doubt Manuela Schönenberger & Stefan Evert QITL, 4 Oct 2002

1. look at the slides The Benefit of DoubtManuela Schönenberger & Stefan EvertQITL, 4 Oct 2002

2. Data from Moira 2-test: p  0 (df=13)(test of idependence = same proportions) http://www.r-project.org/

3. Moira: data by month

4. transition phase Moira: data by month (proportions)

5. Moira: early period vs. late period

6. Moira: early period vs. late period • 2-test: p  0 (df=1) • estimates for proportion q of movement from exact binomial test (95% conf.): • Early: q  97.3% (95.3% – 98.7%) • Late: q  11.1% ( 8.4% – 14.4%)

7. Moira: estimates for early and late period early period: q  97.3% late period: q  11.1%

8. Testing the statistical model • assumptions • the child chooses randomly between clauses with verb movement and no movement • average proportion of clauses with movement is constant within each period • model • number of clauses with mvt in each month is a binomially distributed random variable (success prob. q = MLE for proportion of mvt)

9. Testing the statistical model • test procedure • null hypothesis: variation within each period can be explained by chance • equivalent to independence of rows and columns in the contingency table (by month) • perform 2test on early and late period • results • early period: p  0.696 acceptable • late period: p  0.242 acceptable

10. transition phase A closer look at the transition phase early period: q  97.3% late period: q  11.1%

11. A closer look at the transition phase • compare each month to conf. intervals for proportion q of mvt in early and late period

12. A closer look at the transition phase • compare each month to conf. intervals for proportion q of mvt in early and late period • binomial test reports significant difference for each month (4;11 might be early period) transition phase

13. Eliza: data by month

14. transition phase ?? Eliza: data by month (proportions)

15. Eliza: early period vs. late period

16. Eliza: early period vs. late period • 2-test: p  0.00001 (df=1) • estimates for proportion q of movement from exact binomial test (95% conf.): • Early: q  86.8% (71.9% – 95.6%) • Late: q  36.4% (22.4% – 52.2%)

17. Testing the statistical model • small data problem • not enough data for asymptotic test(normal approximation in 2test is incorrect) • use Fisher's exact test instead • or Monte Carlo simulation (based on 2test) • results • early period: p  0.109 acceptable • late period: p  0.289 acceptable

18. transition phase ?? Eliza: estimates for early and late period early period: q  86.8% late period: q  36.4%

19. A closer look at the transition phase

20. A closer look at the transition phase • binomial test:all four months could belong to early period

21. A closer look at the transition phase • binomial test:all four months could belong to early period • 5;02 might also belong to late period(even though there is always verb mvt!)

22. We've had a very close look at the evidence for verb movement ... ... but we have ignored all ambiguous sentences! Wait a second ...

23. Ambiguous data • so far, we have ignored ambiguous data • this may have distorted the results!

24. Ambiguous data • so far, we have ignored ambiguous data • this may have distorted the results! unambiguouslytype A unambiguouslytype B ambiguous

25. Ambiguous data • so far, we have ignored ambiguous data • this may have distorted the results! unambiguouslytype A unambiguouslytype B ambiguous

26. Child data: non-target consistent • % wenn diefahret so schnell (E:5;02)when these drive so fast • a. % dass dasisch de Uhu (E:5;01)that this is the owlb. % dass erisch es eis (M:4;08)that he is a one • a. % öb'shät am Salot Lüüs (M:4;02)if there has on-the salad greenflyb. % öb ichfind nomel öppis (E:4;10)if I find again something

27. Child data: ambiguous • wenn ichmues lache (E:5;04)when I must laugh • dass-mercha t'Röschti ufsteche (M:4;11)that-one can the rösti up-pick • öb erchämt dete z'Mittag ässe (M:4;06)if he could there to-lunch eat • wenn ichverlüre(M:4;09)when I lose

28. Moira: data by month (incl. ambiguous)

29. transition phase Moira: data by month (proportions)

30. Moira: early period vs. late period

31. Moira: for or against our hypothesis? in favour of new theory(cheating) against new theory(conservative)

32. Moira: for or against our hypothesis? early period: q  97.7% early period: q  83.4% late period: q  8.5% late period: q  31.8% in favour of new theory(cheating) against new theory(conservative)

33. Eliza: data by month (incl. ambiguous)

34. transition phase ??? Eliza: data by month (proportions)

35. Eliza: early period vs. late period

36. Eliza: for or against our hypothesis? in favour of new theory(cheating) against new theory(conservative)

37. Eliza: for or against our hypothesis? early period: q  88.1% early period: q  78.6% late period: q  21.3% late period: q  62.7% in favour of new theory(cheating) against new theory(conservative)

38. References