Quantitative Methods

1. Quantitative Methods Checking the models I: independence

2. Checking the models I: independence Assumptions of GLM

3. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 TREATMNT Coef PREDICTED 1 -1.590 BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 32.316 Checking the models I: independence Assumptions of GLM BACAFTER = BACBEF+TREATMNT (Model Formula) (Model) (Fitted Value Equation or Best Fit Equation)

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

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

6. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models I: independence Assumptions of GLM (Model) Assumptions of GLM Independence Homogeneity of variance Normality of error Linearity/additivity

7. TREATMNT Coef 1 1 BACAFTER = m + bBACBEF + 2 2 +  3 -1 -2 Checking the models I: independence Assumptions of GLM (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 GLM RATE=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

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