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... below: Graph 1 Graph 2 The lines represent the relationships between the response and the covariate within the different groups; in Graph 1 the lines are not forced to be parallel. From the graph, the assumption (for one way ANCOVA) that the lines should be parallel seems reasonable. Also it seems reasonable to assume that the form of the relationship between response and initial score is linear. We can see that the reading condition appears to lie at the top of the graph, the exercise and control groups lie together at the bottom of the graph. This suggests that the reading group has a higher average increase in score than the other two conditions. In Graph 2, the lines have been forced parallel. It is likely that in the population that, once corrected for initial score, the treatment mean increase in score would not all be the same. FORMAL ANALYSIS: To formally test whether ...