Bias-Variance Trade-Off in Continuous Test Norming

Lieke Voncken*, Casper J. Albers, Marieke E. Timmerman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
72 Downloads (Pure)


In continuous test norming, the test score distribution is estimated as a continuous function of predictor(s). A flexible approach for norm estimation is the use of generalized additive models for location, scale, and shape. It is unknown how sensitive their estimates are to model flexibility and sample size. Generally, a flexible model that fits at the population level has smaller bias than its restricted nonfitting version, yet it has larger sampling variability. We investigated how model flexibility relates to bias, variance, and total variability in estimates of normalizedzscores under empirically relevant conditions, involving the skew Studenttand normal distributions as population distributions. We considered both transversal and longitudinal assumption violations. We found that models with too strict distributional assumptions yield biased estimates, whereas too flexible models yield increased variance. The skew Studenttdistribution, unlike the Box-Cox Power Exponential distribution, appeared problematic to estimate for normally distributed data. Recommendations for empirical norming practice are provided.

Original languageEnglish
Pages (from-to)1932-1948
Number of pages17
Issue number8
Early online date13-Jul-2020
Publication statusPublished - 1-Dec-2021


  • assumption violations
  • model assumptions
  • model flexibility
  • skew Studenttdistribution
  • standard linear regression model


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