However, in the same article about imputation, I don't understand why this is not a concern for univariate analysis?
As more of the y-values (dependent variables) get replaced with their means, I know that the sample mean will stay the same (and hence the bias will not be affected). But, it seems to me like this will increase the variance (and standard deviation), regardless of if it is univariate or multivariate. Am I not understanding this correctly?
So, when the wikipedia article says that "mean imputation has some attractive properties for univariate analysis but becomes problematic for multivariate analysis", I don't think that's true. seems to me like they have exactly the same problem?