Download ANOVA vs ANCOVA notes

Class Note
Thursday, October 1, 2015
9:27 AM
ANCOVA (Analysis of Covariance)
- Use ANCOVA for the same type of designs you would use ANOVA
- Typically, ANCOVA is a more powerful statistical test
- Allows you to statistically equalize the different groups for the levels of the independent variable
○ Use a procedure for random assignment of groups in an effort to limit extraneous variables
In ANOVA
- F ratio = (individual differences + experimenter error + independent variable effect)/(individual
differences + experimenter error)
If we could do something that decreased chance variability (individual differences + experimenter error)
without decreasing independent variable then we could increase F
- Bigger F = smaller sig = greater power to reject null hypothesis
ANCOVA changes the way variance is computed
- Sum(Y-M)^2
- "Y-M" = each score subtracted from the mew
To do ANCOVA we need:
- Factor with levels
- Dependent variable score for each subject
- A covariate score for each subject
○ Variables related to dependent variable but not related to the independent variable (i.e. leg
length)
○ Information is measured before the experiment
○ Covariate refers to quality, not category
ANCOVA -> compute a regression line between covariate and dependent variable
- Y=bX+a
- Take all individual Y scores and subtract from the point in the line that corresponds to their X
○ Smaller distance from the line
- Variance is coputed by Y - Y(^ on top)
- Y(^) is the point on the line predicted for the X
○ Y - Y(^) =< Y - M
▪ In general, "Y = - Y(^) =< Y - M" means a bigger F
As long as there is at least a small relationship between covariate and dependent variable, "Y - Y(^)
=< Y - M" doesn't yield 0
Fall 2015 Page 1