Which statement describes grand mean centring?

Which statement describes grand mean centring?

• A. Subtract the grand mean of the variable from every score.
• B. Subtract the mean of the scores within the sample from the scores.
• C. Multiply each score by the grand mean.
• D. Subtract the minimum score from each score.

Answer: (A)

Grand mean centering means adjusting each score by removing the overall average across all observations, so the transformed values are centered around zero. Specifically, you subtract the grand mean from every score, which makes the new variable have a mean of zero. This helps in regression, especially with interaction terms, because it makes the interpretation of main effects clearer and can reduce multicollinearity between predictors. The statement that describes subtracting the grand mean from every score is the correct description of this process. The other options describe different actions—centering by a within-sample mean (group-mean centering), multiplying by a constant, or subtracting the minimum value—which do not implement grand-mean centering.

Grand mean centering means adjusting each score by removing the overall average across all observations, so the transformed values are centered around zero. Specifically, you subtract the grand mean from every score, which makes the new variable have a mean of zero. This helps in regression, especially with interaction terms, because it makes the interpretation of main effects clearer and can reduce multicollinearity between predictors. The statement that describes subtracting the grand mean from every score is the correct description of this process. The other options describe different actions—centering by a within-sample mean (group-mean centering), multiplying by a constant, or subtracting the minimum value—which do not implement grand-mean centering.