# B AD 6243: Applied Univariate Statistics - PowerPoint PPT Presentation

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B AD 6243: Applied Univariate Statistics. Analysis of Covariance (ANCOVA) Professor Laku Chidambaram Price College of Business University of Oklahoma. ANCOVA. Purpose Reduce within group error variance Eliminate confounds Assumptions All assumptions of ANOVA

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B AD 6243: Applied Univariate Statistics

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## B AD 6243: Applied Univariate Statistics

Analysis of Covariance (ANCOVA)

Professor Laku Chidambaram

University of Oklahoma

### ANCOVA

• Purpose

• Reduce within group error variance

• Eliminate confounds

• Assumptions

• All assumptions of ANOVA

• Covariates are not significantly different across groups

• Covariate and dependent variable have similar relationships across the groups (i.e., homogeneity of regression slopes)

### An Example

• A program to help smokers quit smoking wants to test the effectiveness of two types of interventions—nicotine gum (0) vs. nicotine patch (1)—for smokers of both genders—males (0) and females (1)

• At the end of the study, blood oxygen levels are measured for all subjects and converted to an OxLevel index (a measure of effectiveness)

• We also believe that the amount of exercise affects OxLevel, so ExLevel is included in our model

• Assume there are two subjects (!) in each group

### Partitioning Variance (ANOVA)

Variance due to Treatment

(Factor 1)

Error Variance

31%

46%

15%

8%

Variance due to Interaction

(Treatment x Gender)

Variance due to Gender

(Factor 2)

### ANCOVA as Regression

• Independent variables include the factors, interactions and the covariates; the dependent variable remains the same

• The factors and the interactions are categorical (dichotomous) while the dependent variable and the covariates are (generally) continuous

• The regression equation would be expressed as follows:

Y = 0 + 1X1 + 2X2 + 3X1X2 + 4X4 + I

(where X1=Treatment, X2=Gender, X1X2= Interaction X4=Exercise)

Data set used in analysis: