Which statement describes group mean centring?

• A. Subtracting the grand mean from each score.
• B. Subtracting the mean for the entire sample from each score.
• C. Subtracting the maximum score within the group from each score.
• D. Subtracting the mean of the scores for the group to which that score belongs from that score.

Answer: (D)

Group mean centering involves taking each observation and subtracting the mean of its own group from that observation. This transforms the predictor into a measure of how far a score deviates from its group's average, isolating within-group variation. With this centering, the model’s coefficients reflect relationships that occur within groups rather than differences between groups, because the group’s overall level no longer contributes to the predictor’s value.

Subtracting the grand mean would create grand-mean centering, which mixes information across groups rather than focusing on within-group deviations. Subtracting the maximum score within the group or subtracting a global sample mean do not provide the intended within-group centering. The described approach—subtracting the mean of the scores for the group to which that score belongs from that score—is exactly group mean centering.