Quantitative Methods Checking the models I independence Checking

Checking the models I: independence Assumptions of GLM

Checking the models I: independence Assumptions of GLM BACAFTER = BACBEF+TREATMNT (Model Formula) BACAFTER

Checking the models I: independence Assumptions of GLM BACAFTER = m + b BACBEF

Checking the models I: independence Independence in principle

Checking the models I: independence Heterogeneous data

Checking the models I: independence Repeated measures

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

Checking the models I: independence Repeated measures name C 100 ’wtg’ let wtg=LOGWT 20

Checking the models I: independence Repeated measures GLM LOGWT 60 RATE = DIET; MANOVA;

Checking the models I: independence Nested data

Checking the models I: independence Detecting non-independence In principle: would knowing the error for

Checking the models I: independence Last words… • Independence is a key assumption, and

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Quantitative Methods Checking the models I: independence

Checking the models I: independence Assumptions of GLM

Checking the models I: independence Assumptions of GLM BACAFTER = BACBEF+TREATMNT (Model Formula) BACAFTER = m + b BACBEF + (Model) TREATMNT Coef 1 1 2 2 3 - 1 - 2 + TREATMNT Coef PREDICTED 1 -1. 590 BACAFTER = -0. 013 + 0. 8831 BACBEF + 2 -0. 726 3 2. 316 (Fitted Value Equation or Best Fit Equation)

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

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

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

Checking the models I: independence Independence in principle

Checking the models I: independence Heterogeneous data

Checking the models I: independence Repeated measures

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

Checking the models I: independence Repeated measures name C 100 ’wtg’ let wtg=LOGWT 20 -LOGWT 3 glm wtg=diet GLM RATE=DIET LET LET LET K 3=3 -31/3 ! 31/3 is the average of K 8=8 -31/3 ! 3, 8 and 20 K 20=20 -31/3 K 1=K 3**2+K 8**2+K 20**2 RATE=(K 3*LOGWT 3+K 8*LOGWT 8+K 20*LOGWT 20)/K 1

Checking the models I: independence Repeated measures

Checking the models I: independence Repeated measures GLM LOGWT 60 RATE = DIET; MANOVA; NOUNIVARIATE.

Checking the models I: independence Nested data

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

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