Why and When You Should Avoid Using z-scores in Graphs Displaying Profile or Group Differences

Area of Science:

• Psychology
• Statistics
• Quantitative Research Methods

Background:

• Person-oriented studies frequently employ z-standardized scores for cluster analysis and group difference comparisons.
• Z-standardization is often applied without considering its potential limitations in these specific research contexts.

Purpose of the Study:

• To critically evaluate the use of z-standardized scores in person-oriented methods.
• To identify and explain the problematic and misleading aspects of z-scores in cluster analysis and group comparisons.
• To propose alternative, less problematic methods for data normalization and analysis.

Main Methods:

• The study reviews theoretical arguments and provides illustrative examples of how z-scores can lead to distortions.
• It contrasts the assumptions of z-standardization with the typical characteristics of data in person-oriented research.
• Alternative normalization techniques are discussed and recommended.

Main Results:

• Z-standardization distorts the ratio of differences between groups and variables.
• It leads to a loss of information regarding item endorsement and rejection.
• The psychological meaning of z-scores is not consistent across samples and variables, impacting group assignments and subsequent analyses.

Conclusions:

• Z-standardized scores should be avoided in person-oriented research due to inherent distortions and logical mismatches with within-person analyses.
• Alternative normalization methods, such as using raw scores or range-based transformations, offer more accurate and meaningful results.
• Researchers should carefully consider normalization techniques to ensure methodological alignment with person-oriented research questions.