Lab 5 instruction

 a collection of statistical methods to compare several groups according to their means on a quantitative response variable  Two-Way ANOVA two factors are used consider “main effect” and “interaction effect”

 Response: Blood Alcohol Content (BAC)  Factors: ◦ Gender(GEN) ◦ Alcohol Consumption (ALC)  Factor levels: ◦ GEN: 1=Male; 0=Female ◦ ALC: 1=1 drink; 2=2 drinks; 4=4 drinks  Main effect of GEN, main effect of ALC, and their interaction Example

 Table of marginal means (contingency table)  In SPSS: Analyze  Compare Means  Means /Or General linear models  descriptive stat Explore the difference in average response across both factors.

 Response: in Dependent list  Factors: in independent list of two seperate layers e.g. Table of marginal means (contingency table)

 Interpret

 Plots of marginal means (profile plot)  In SPSS: Graphs  legacy dialogs  Line  multiple /Or GLM  univariate  (plots) Explore the difference in average response across both factors.

 Profile plot with lines representing gender e.g. Plot of marginal means (profile plot)

 Interpretation: ◦ 6 points ◦ Effect of gender ◦ Effect of drink consumption ◦ Interaction (parallel or crossed) e.g. Plot of marginal means (profile plot)

 Clustered boxplot  In SPSS: Graphs  legacy dialogs  Boxplot  Clustered Explore the difference in average response across both factors.

 Clustered boxplot with clusters defined by gender e.g. Clustered boxplot

General Linear Model (GLM)-Assumptions  Independent samples  Normality: ◦ Boxplot ◦ QQ plot  Equal standard deviation (variance): ◦ Boxplot ◦ Summary statistics (rule of thumb: the ratio of the largest s.d. over the smallest s.d. is less than 2)

General Linear Model (GLM)  Univariate GLM is the general linear model now often used to implement such essential statistical procedures as regression and ANOVA. In particular, the procedure can be used to carry out two-way analysis of variance.  Procedure: Analyze  General Linear Model  Univariate (defaulted: model with Interactions)

GLM: Non-additive model output

 In columns “SS” and “df” ◦ Corrected total = corrected model + error ◦ Corrected model=GEN + ALC + GEN*ALC  The column “F” contains the value of the f statistic for each effect. The value of F is computed as follows: GLM: Non-additive model output

Hypothesis test : no interaction between GEN and ALC

Equivalent to the regression models: Since the interaction term is not significant, we tend to modify the model. the model without the interaction term: additive model

GLM: Define additive model

GLM: Additive model output & equivalent regression model

GLM - Options  Model ： define the model, Include intercept or not  Contrasts: The linear combination of the level means  Profile Plots: the plot of estimated means  Post Hoc  Save  Options

 Profile Plots: different from the one obtained with line chart  This plots estimated means form the model GLM - Options

 Define dummy variables  Write down estimated model equation  Use extra-sum-of-squares F-test for testing interaction term  Interpret meaning of estimated coefficient, t- test on coefficients and their 95% CI Equivalent regression models and tests

 estimated regression model with interaction term (full non-additive model) Equivalent regression models and tests

 estimated regression model with NO interaction term (additive model) Equivalent regression models and tests

 Construct extra-of-sum F-test use the above two ANOVA tables,  In the regression model with NO interaction term, interpret meaning of, and its CI.  Is “GEN” effective in predicting BAC? (t-test on ) Equivalent regression models and tests

 Linear combination of mean difference in BAC for male V.S. female  Substitute ’s by corresponding ’s Note on Q3 (b)

 Rate of increase in mean BAC for an increase in drinks consumption  Thus, in Q3 (c) ◦ rate (1to2) =, rate (2to4) =  In Q7 (c) ◦ rate (1to2) =, rate (2to4) = Note on Q3 (c) and Q7 (c)