As the question said, when I conducted a two-way ANCOVA （pre-test served as covariate） after confirming the homogeneity of regression slopes assumption, a statistical significance was found on the covariates (pre-test score). In this case, how can I interpret the results?
Analysis of covariance is essentially analysis of variance in which differences between levels of a facftor are tested after controlling for other variables, termed covariates. The response variable and he covariate are assumed to be related in some way, and from the estimated relationship, the subject's reponse values are adjusted in an attempt to account for factor level differences in cavariates. If the covariates is significant, ,this indicated the adjustment was effective.
The results show that there is a significant correlation between the pre- and post-test scores, which is to be expected. If the coefficient is positive, the scores increased, while a negative coefficient indicates a decrease over time.
In an ANCOVA test the covariate does not vary among the groups of the categorical factor or factors. Assuming that the interaction term is not significant then the assumption is not violated. If the interaction were significant,then you need to use a different approach to analyze this data, such as a mixed model.
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