Quantitative Methods Checking the models II: the other three assumptions

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 BACAFTER = BACBEF (Model Formula) (Model) (Fitted Value Equation or Best Fit Equation)

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

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

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

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

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

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

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

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

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

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

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

Model Criticism Checking the models II: the other 3 assumptions

Model Criticism Checking the models II: the other 3 assumptions

Model Criticism Checking the models II: the other 3 assumptions

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

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

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

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

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

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

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

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

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

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

Non-linearity

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

Example Checking the models II: the other 3 assumptions

Example Checking the models II: the other 3 assumptions

Example Checking the models II: the other 3 assumptions

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

Hints Checking the models II: the other 3 assumptions

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

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)

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