lab 5 instruction. a collection of statistical methods to compare several groups according to their...
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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 usedconsider “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
ExampleExample
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)
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
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
GLM: Non-additive model output
Hypothesis test : no interaction between GEN and ALC
H0
Equivalent to the regression Equivalent to the regression models:models:
H0 :4 5 0
HA : not both are zeros
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
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alcalcgenALCGENBAC
ALCGENBAC
GLM: Additive model output & equivalent regression model
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alcalcgenALCGENBAC
alcalcALCGENBAC
GLM: Additive model output & equivalent regression model
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alcalcgenALCGENBAC
genALCGENBAC
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
1
1
Linear combination of mean difference in BAC for male V.S. female
Substitute ’s by corresponding ’s
Note on Q3 (b)
33421421 fffmmm
Y
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)
2
3 2
2
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