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Is it typical for group means of composite z-scores to have means with values of the same magnitude but opposite signs?

I developed a composite score by converting four items to z-scores, then I summed up the z-scores to form a composite measure. However, when I've calculated means to compare finding for two ...
2
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References for creating Neuropsychological composite scores

I am a doctoral student in clinical neuropsychology, and am in the process of creating z-unit weighted composite scores based on a battery of ability tests (i.e., attention/executive functions ...