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Understanding Analysis of Covariance (ANCOVA)

By HWA | Publish On: January 12, 2011 | Posted In:

Similar to an ANOVA, ANCOVA examines the effect of an Independent on Dependent variable. The Independent variable is nominal (categorical) and Dependent variable is interval (continuous). In real life, there are many other variables that can affect the Dependent Variable such as Confounding Variables.

Hypothesis testing (ANCOVA)
• Null Hypothesis (Ho): There is no significant difference between treatment conditions in the Independent Variable on the Dependent Variable
• Ho: M1=M2=M3……=MK
• Alternative Hypothesis (Ha): There is significant difference between treatment conditions in the Independent Variable on the Dependent Variable
• Ha: Means are not equal
• M1=M2=M3……=MK =Means of the different groups

ANCOVA Assumptions
• Random Sample: There was no selection bias in forming the different groups.
• Normality: Assumes that here are no outliers in the performance of participants and skewness is near zero
• Homogeneity of variance (Levene’s test): the dependent variable must have equal variances. If Levene’s test is not significant, homogeneity of variances is met
• Independence Assumption: assumes that a particular person’s performance should not be influenced by confounds or other experimental groups.
• There is a linear relationship between the DV and covariates
• Covariate is reliable and measured without error

ANCOVA example
• A researcher is trying to investigate the effects of being in different academic programs (general, academic and vocational) on a students’ performance on the writing section of a standardized exam. The researcher uses the students’ performance on the reading section of a standardized exam as a covariate.

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This is in continuation with our previous Statistics article.

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