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B AD 6243: Applied Univariate StatisticsPowerPoint Presentation

B AD 6243: Applied Univariate Statistics

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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
- Covariates are not significantly different across groups
- Covariate and dependent variable have similar relationships across the groups (i.e., homogeneity of regression slopes)

BAD 6243: Applied Univariate Statistics

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

BAD 6243: Applied Univariate Statistics

ANOVA vs. ANCOVA

BAD 6243: Applied Univariate Statistics

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)

BAD 6243: Applied Univariate Statistics

Partitioning Variance (ANCOVA)

BAD 6243: Applied Univariate Statistics

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:

BAD 6243: Applied Univariate Statistics

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