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

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B AD 6243: Applied Univariate Statistics

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B ad 6243 applied univariate statistics

B AD 6243: Applied Univariate Statistics

Analysis of Covariance (ANCOVA)

Professor Laku Chidambaram

Price College of Business

University of Oklahoma


Ancova

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

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


Testing assumptions of ancova

Testing Assumptions of ANCOVA


Anova vs ancova

ANOVA vs. ANCOVA

BAD 6243: Applied Univariate Statistics


Partitioning variance anova

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

Partitioning Variance (ANCOVA)

BAD 6243: Applied Univariate Statistics


Ancova as regression

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


Regression results

Regression Results


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