Why and when you should avoid using z-scores in graphs displaying profile or group differences

Many person-oriented studies use <i>z</i>-standardized scores before conducting cluster analyses and/or before displaying group differences. This article summarizes reasons why <i>z-</i> standardized scores can often be problematic and misleading in person-oriented methods. The article shows examples illustrating why and how the use of <i>z</i>-scores in group classification and comparisons can be misleading, and proposes less problematic methods. Reasons why <i>z</i>-standardized scores should be avoided when classifying or displaying differences between clusters, profiles, and other groups are: The ratio of the difference between two groups is distorted in <i>z</i>-scores.The ratio of the difference between two variables is distorted in <i>z</i>-scores.Information about item endorsement and item rejection is lost.The psychological meaning of a given <i>z</i>-score does not compare across samples and variables.Group assignments can be misleading if <i>z</i>-scores are used to assign individuals to groups.The group size and group frequency may be affected if <i>z</i>-scores instead of raw scores are used to assign individuals to groups.Group differences in further outcome variables can change if <i>z</i>-scores instead of raw scores are used to assign individuals to groups.Alternative normalization techniques perform better than <i>z</i>-standardization in cluster analyses.<i>z</i>-standardization relies on homogeneity assumptions, including unimodality, but distributions analysed in person-oriented research are often multimodal.Person-oriented methods typically examine within-person patterns to answer research questions about within-person phenomena, whereas <i>z</i>-standardization typically refers to between-person variation, which creates a logical mismatch between theory and method. Alternatives to using <i>z</i>-scores in graphs displaying profiles and group differences are using raw scores or using scale transformations that use the range, not the standard deviation in the normalization.