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Chapter 7: ANCOVA (Self-Study)

1. Chapter 7: ANCOVA (Self-Study). Objectives. Identify typical scenarios in ANCOVA. Fit ANCOVA models both with and without interactions. N-Way ANOVA versus ANCOVA. 7.01 Quiz.

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Chapter 7: ANCOVA (Self-Study)

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  1. 1 Chapter 7: ANCOVA (Self-Study)

  2. Objectives • Identify typical scenarios in ANCOVA. • Fit ANCOVA models both with and without interactions.

  3. N-Way ANOVA versus ANCOVA

  4. 7.01 Quiz • The effect of machines on fabric strength is to be studied. Engineers are concerned that yarn thickness has an effect on fabric strength, but this cannot be controlled. An ANCOVA is appropriate. • Match the variables on the left to their roles on the right. • 1. fabric strength • 2. machine • 3. yarn thickness A. categorical factor B. response variable C. covariate factor

  5. 7.01 Quiz – Correct Answer • The effect of machines on fabric strength is to be studied. Engineers are concerned that yarn thickness has an effect on fabric strength, but this cannot be controlled. An ANCOVA is appropriate. • Match the variables on the left to their roles on the right. • 1. fabric strength • 2. machine • 3. yarn thickness • 1-B, 2-A, 3-C A. categorical factor B. response variable C. covariate factor

  6. ANCOVA Situations ANOVA ANCOVA, ANCOVA, no interaction with interaction

  7. Board Strength Example

  8. Saw Blade Example

  9. ANCOVA Model with No Interaction Type of Board Tensile Strength Base Level Specific Density Unexplained Variation = + + + Yik = µ + τi+ βXik+ εik

  10. ANCOVA with No Interactions Y1k= µ + τ1 + βX1k + ε1k equal slopes Y2k= µ + τ2 + βX2k + ε2k

  11. ANCOVA with Interactions Y1k= µ + τ1 + β1X1k + ε1k unequal slopes Y2k= µ + τ2 + β2X2k + ε2k

  12. 7.02 Multiple Choice Poll • Suppose that the ANCOVA model yields two slightly different beta estimates. You would expect to see which of the following? • A model with an interaction term included where the interaction is nonsignificant • A model with an interaction term included where the interaction is significant • A model with no interaction specified

  13. 7.02 Multiple Choice Poll – Correct Answer • Suppose that the ANCOVA model yields two slightly different beta estimates. You would expect to see which of the following? • A model with an interaction term included where the interaction is nonsignificant • A model with an interaction term included where the interaction is significant • A model with no interaction specified

  14. Fitting an ANCOVA Model • This demonstration illustrates the concepts discussed previously.

  15. Exercise • This exercise reinforces the concepts discussed previously.

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