To check difference of post test between test group and control group by controlling pre test score.
I read that ANCOVA is based on the assumption that the means of the covariate are equal across groups. In other words, the covariate (pre-test scores) should not differ significantly between groups. If there is a significant difference in the covariate across groups, it suggests that the pre-test scores themselves differ by group, which could bias the analysis results.
However, what I understand is that ANCOVA is conducted to control for covariates. If the pre-test (covariate) is already same, why do we need to perform ANCOVA to control covariate? it is already same.. Isn't it the same as an independent t-test? Wouldn't it be more logical to say: despite the difference between the two groups (experimental, control) in the pretest, set it as a covariate to see the difference between the two groups in the posttest?
Point of clarification - ANCOVA does not assume groups have equal pretest means . Rather, ANCOVA assumes the slope between the covariate and outcome is the same across groups.
It's not problematic if groups significantly differ on the pretest scores. The issue is whether the covariate (pretest scores) significantly interacts with the outcome variable. You can check this by including a factor*covariate interaction term in the model.
Blaine Tomkins Oh okay! slope must be same, which means, there is no interaction becuase If an interaction exists, it means that the covariate affects different group differently. Am I correct?
Covariates aren't always pretests. Sometimes they're measures which could account for significant variance in the dependent variable. The covariate then functions to reduce error variance, making testing of the independent variable more powerful, i.e. more likely to show as significant or more significant, e.g. p< .01 rather than p < .05.
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