1. Quantitative Methods Checking the models I: independence

2. Assumptions of GLM

3. Checking the models I: independence 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)

4. Checking the models I: independence Assumptions of GLM BACAFTER = BACBEF+TREATMNT TREATMNT Coef 1  1 BACAFTER =  + BACBEF + 2  2 +  3 - 1 - 2 (Model Formula) (Model)

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

6. Checking the models I: independence 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

7. Checking the models I: independence 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

8. Checking the models I: independence Independence in principle

9. Checking the models I: independence Heterogeneous data

10. Checking the models I: independence Heterogeneous data

11. Checking the models I: independence Heterogeneous data

12. Checking the models I: independence Heterogeneous data

13. Checking the models I: independence Heterogeneous data

14. Checking the models I: independence Heterogeneous data

15. Checking the models I: independence Repeated measures

16. Checking the models I: independence Repeated measures

17. Checking the models I: independence Repeated measures

18. Checking the models I: independence Repeated measures

19. Checking the models I: independence Repeated measures Single summary approach Multivariate approach Few summaries approach

20. Checking the models I: independence Repeated measures name C100 ’wtg’ let wtg=LOGWT20-LOGWT3 glm wtg=diet LET K3=3-31/3 ! 31/3 is the average of LET K8=8-31/3 ! 3, 8 and 20 LET K20=20-31/3 LET K1=K3**2+K8**2+K20**2 LET RATE=(K3*LOGWT3+K8*LOGWT8+K20*LOGWT20)/K1 GLM RATE=DIET

21. Checking the models I: independence Repeated measures

22. Checking the models I: independence Repeated measures GLM LOGWT60 RATE = DIET; MANOVA; NOUNIVARIATE.

23. Checking the models I: independence Nested data

24. Checking the models I: independence Nested data

25. Checking the models I: independence Detecting non-independence In principle: would knowing the error for one or more datapoints help you guess the error for some other datapoint? Experiments: Does the datapoint correspond to the level of randomisation? Observations: Are there groups of datapoints which are very likely to have similar residuals? Be suspicious of - Too many datapoints - Implausible results - Repeated measures

26. Checking the models I: independence Last words… Independence is a key assumption, and is the most problematic in practice Always be alert to possible violations Know what can be done at the analysis stage Realise that mistakes at the design stage are often unrecoverable at analysis Checking the models II: the other three assumptions Read Chapter 9