**Admissable statistics and latent variable theory**

**Annemarie Zand Scholten**

Psychological Methodology

Department of Psychology

FMG, University of Amsterdam

**Supervisors:** Prof. dr H.L.J. van der Maas (University of Amsterdam), dr D. Borsboom (University of Amsterdam), dr P. Koele (University of Amsterdam)

**Project running from:** 1 April 2005 – 1 September 2010

**Summary:
**Does the appropriateness of statistical analyses depend on the measurement level of the variables on which these analyses are carried out? Measurement theorists are generally of the opinion that this is the case; the measurement level of variables determines the class of appropriate statistics. Several statisticians have, however, claimed that this limitation is unfounded and that it has adverse scientific consequences. The disagreement between these camps is known as the admissible statistics controversy. Although discussants in this controversy disagree on virtually everything, they share a core assumption: namely, that measurement and statistical analyses are separate endeavors. However, in an important class of measurement models, known as latent variable models, measurement and statistical theory are intertwined to such a degree that it is difficult to say where one begins and the other ends. In the present research, the admissible statistics problem is formulated and analyzed in terms of latent variable theory. This yields a quite different view of what the problem actually is; namely, a problem that occurs because statistical analyses assume that variables are errorless measures of the theoretical attributes involved, while measurement models usually view these same variables as imperfect indicators of these attributes. Thus, the admissible statistics problem becomes a question of robustness: Under which conditions is it possible to ignore measurement error and equate observed scores to theoretical attributes? This question is investigated through mathematical analysis and simulation studies. Second, alternative methodes of analysis, that may be used to address measurement and statistical issues at the same time, are evaluated for their potential in solving the admissible statistics problem; specifically, the use of multi group models with mean structures in factorial designs is investigated in this respect.

**Date of defence:** 21 January 2011

**Title of thesis**: Formele meettheorie bruikbaar in psychologie voor inschatting foute conclusie

**Digital Academic Repository: **http://dare.uva.nl/record/366790