## Abstract

The sum score on a psychological test is, and should continue to be, a tool central in psychometric practice. This position runs counter to several psychometricians’ belief that the sum score represents a pre-scientific conception that must be abandoned from psychometrics in favor of latent variables. First, we reiterate that the sum score stochastically orders the latent variable in a wide variety of much-used item response models. In fact, item response theory provides a mathematically based justification for the ordinal use of the sum score. Second, because discussions about the sum score often involve its reliability and estimation methods as well, we show that, based on very general assumptions, classical test theory provides a family of lower bounds several of which are close to the true reliability under reasonable conditions. Finally, we argue that eventually sum scores derive their value from the degree to which they enable predicting practically relevant events and behaviors. None of our discussion is meant to discredit modern measurement models; they have their own merits unattainable for classical test theory, but the latter model provides impressive contributions to psychometrics based on very few assumptions that seem to have become obscured in the past few decades. Their generality and practical usefulness add to the accomplishments of more recent approaches.

Original language | English |
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Pages (from-to) | 84-117 |

Number of pages | 34 |

Journal | Psychometrika |

Volume | 89 |

Issue number | 1 |

DOIs | |

Publication status | E-pub ahead of print - 17 Apr 2024 |

## Keywords

- classical test theory
- factor analysis model
- item response theory
- latent variable
- lower bound to reliability
- network models
- reliability
- sum score