Which term describes a non-orthogonal planned contrast that compares the mean of each group to the overall mean?

Which term describes a non-orthogonal planned contrast that compares the mean of each group to the overall mean?

• A. Deviation contrast
• B. Difference contrast
• C. Direct oblimin
• D. Discrete variable

Answer: (A)

Focusing on how to test specific hypotheses about group means in ANOVA, a contrast is a linear combination of the group means with coefficients that sum to zero. A deviation contrast is the one that compares each group’s mean to the grand mean, so the test asks whether a particular group deviates from the overall average. Because these contrasts are anchored to the grand mean and the set of coefficients is not guaranteed to be orthogonal to other contrasts, they are typically non-orthogonal. For example, with several groups, one deviation contrast might emphasize how far a given group is from the overall mean, and another would do the same for a different group, yielding a non-orthogonal set of tests. The other terms don’t describe this idea: a difference contrast involves comparing groups in a stepwise or adjacent way, direct oblimin is a rotation method used in factor analysis, and a discrete variable is a type of variable, not a contrast.

Focusing on how to test specific hypotheses about group means in ANOVA, a contrast is a linear combination of the group means with coefficients that sum to zero. A deviation contrast is the one that compares each group’s mean to the grand mean, so the test asks whether a particular group deviates from the overall average. Because these contrasts are anchored to the grand mean and the set of coefficients is not guaranteed to be orthogonal to other contrasts, they are typically non-orthogonal. For example, with several groups, one deviation contrast might emphasize how far a given group is from the overall mean, and another would do the same for a different group, yielding a non-orthogonal set of tests. The other terms don’t describe this idea: a difference contrast involves comparing groups in a stepwise or adjacent way, direct oblimin is a rotation method used in factor analysis, and a discrete variable is a type of variable, not a contrast.