1. Quantitative Methods Checking the models II: the other three assumptions

2. Checking the models II: the other 3 assumptions Assumptions of GLM BACAFTER = BACBEF+TREATMNT TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 TREATMNT Coef PREDICTED 1 -1.590 BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 3 2.316 (Model Formula) (Model) (Fitted Value Equation or Best Fit Equation)

3. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Checking the models II: the other 3 assumptions

4. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

5. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

6. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

7. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

8. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

9. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

10. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

11. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

12. Assumptions of GLM TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

13. Are the assumptions likely to be true? Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity Checking the models II: the other 3 assumptions

14. Model Criticism Checking the models II: the other 3 assumptions

15. Model Criticism Checking the models II: the other 3 assumptions

16. Model Criticism Checking the models II: the other 3 assumptions

17. Transformations and Homogeneity Checking the models II: the other 3 assumptions

18. Transformations and Homogeneity Checking the models II: the other 3 assumptions

19. Transformations and Homogeneity Checking the models II: the other 3 assumptions

20. Transformations and Homogeneity Checking the models II: the other 3 assumptions

21. Transformations and Homogeneity Checking the models II: the other 3 assumptions

22. Transformations and Homogeneity Checking the models II: the other 3 assumptions

23. Transformations and Homogeneity Checking the models II: the other 3 assumptions

24. Transformations and Homogeneity Checking the models II: the other 3 assumptions None, or linear Square root Log Negative inverse

25. Non-linearity Checking the models II: the other 3 assumptions

26. Non-linearity Checking the models II: the other 3 assumptions

27. Non-linearity

28. Checking the models II: the other 3 assumptions Non-linearity

29. Example Checking the models II: the other 3 assumptions

30. Example Checking the models II: the other 3 assumptions

31. Example Checking the models II: the other 3 assumptions

32. Example Checking the models II: the other 3 assumptions MTB > let LOGDEN=log(DENSITY)

33. Hints Checking the models II: the other 3 assumptions

34. Hints Checking the models II: the other 3 assumptions Morphometric data: log Count data: square root Proportional data: angular Survival data: negative inverse Don’t be too picky

35. Selecting a transformation Checking the models II: the other 3 assumptions With covariates, consider transforming X too Continuous y-variable - varying strengths Increasing strength: none, square root, log, negative inverse Proportions - root arcsin Counts - square root Based on homogenising the error variance Go through the model criticism process again (and if necessary again and again)

36. Last words… You should always check assumptions as much as you can using the techniques of model criticism Transformations can help to ‘cure’ failures to meet assumptions Always repeat model criticism after transforming Homogeneity of variance is the priority for transformations Model selection I: principles of model choice and designed experiments Read Chapter 10 Checking the models II: the other 3 assumptions