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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