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

Abstract

Many person-oriented studies use z-standardized scores before conducting cluster analyses and/or before displaying group differences. This article summarizes reasons why z-standardized scores can often be problematic and misleading in person-oriented methods. The article shows examples illustrating why and how the use of z-scores in group classification and comparisons can be misleading, and proposes less problematic methods. Reasons why z-standardized scores should be avoided when classifying or displaying differences between clusters, profiles, and other groups are:

(1) The ratio of the difference between two groups is distorted in z-scores.

(2) The ratio of the difference between two variables is distorted in z-scores.

(3) Information about item endorsement and item rejection is lost.

(4) The psychological meaning of a given z-score does not compare across samples and variables.

(5) Group assignments can be misleading if z-scores are used to assign individuals to groups.

(6) The group size and group frequency may be affected if z-scores instead of raw scores are used to assign individuals to groups.

(7) Group differences in further outcome variables can change if z-scores instead of raw scores are used to assign individuals to groups.

(8) Alternative normalization techniques perform better than z-standardization in cluster analyses.

(9) z-standardization relies on homogeneity assumptions, including unimodality, but distributions analysed in person-oriented research are often multimodal.

(10) Person-oriented methods typically examine within-person patterns to answer research questions about within-person phenomena, whereas z-standardization typically refers to between-person variation, which creates a logical mismatch between theory and method.

Alternatives to using z-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.