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ANCOVA

ANCOVA. One continuous Y variable. One or more continuous X variables (covariates). One or more class variables (treatments). Model: (Y-GM Y ) = (Y-Y’) + B (X-GM X ) + e Y = m j + B (X- GM X ) + e. Use of ANCOVA. Increase sensitivity of ANOVA.

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ANCOVA

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  1. ANCOVA • One continuous Y variable. • One or more continuous X variables (covariates). • One or more class variables (treatments). • Model:(Y-GMY) = (Y-Y’) + B (X-GMX) + eY = mj + B (X- GMX) + e AGR206

  2. Use of ANCOVA • Increase sensitivity of ANOVA. • Adjust the treatment means to what they would be if all were at the average value of X. • In MANOVA (not considered any further). AGR206

  3. Assumptions • Normal, independent and equal-variance errors. • X is not affected by treatments. • Relationship between Y and X’s does not need to be linear. • Homogeneity of slopes. The model that relates Y to X’s must be the same for all groups (except for intercept). AGR206

  4. Example: 3 treatments New sales Previous sales AGR206

  5. Uncorrected ANOVA AGR206

  6. ANCOVA AGR206

  7. HW06 Solution AGR206

  8. HW06 Solution AGR206

  9. HW06 Solution AGR206

  10. HW06 Solution AGR206

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