Analysis of Covariance (ANCOVA)

Analysis of Covariance (ANCOVA)

Analysis of Covariance (ANCOVA)

• add continuous covariate

• reduce unexplained variance
• increase power of test

Analysis of Covariance (ANCOVA)

Analysis of Covariance (ANCOVA)

Assumptions

1. Normality (residuals)
2. Homogeneity of variance (residuals)
3. Independence
4. Homogeneity of slopes

Homogeneity of Slopes

• no interaction effects

Analysis of Covariance (ANCOVA)

Assumptions

1. Normality (residuals)
2. Homogeneity of variance (residuals)
3. Independence
4. Homogeneity of slopes
5. Similar covariate range

Covariate range

Analysis of Covariance (ANCOVA)

Design balance

• ANCOVA designs are inherently imbalanced
• Need to use Type II or III SS

Analysis of Covariance (ANCOVA)

Offsets

• Standardize the response for a covariate
• Does not cost a degree of freedom

Worked Examples

Format of partridge1.csv data file

TREATMENT THORAX LONGEV Preg8 0.64 35 Preg8 0.68 37 Preg8 0.68 49 .. .. .. TREATMENT Categorical listing of the number and sort of female partners(None - no female partners, Preg1 - one pregnant female partner, Preg8 - eight pregnant partners, Virg1 - one virgin female, Virg8 - eight virgin females) THORAX Continuous covariate, the length of the thorax (mm) LONGEV Longevity of male fruitflies. Response variable.

> partridge <- read.csv('../data/partridge1.csv', strip.white=T)
> head(partridge)

  TREATMENT THORAX LONGEV
1     Preg8   0.64     35
2     Preg8   0.68     37
3     Preg8   0.68     49
4     Preg8   0.72     46
5     Preg8   0.72     63
6     Preg8   0.76     39