Methodology and Statistics

Social and Behavioral Sciences

Tilburg University

**Supervisors
**Prof. K. Sijtsma & Prof. L. A. van der Ark

On April 12th, 2017, Hannah Oosterhuis defended her thesis entitled

**Regression-Based Norming for Psychological Tests and Questionnaires**

**Project**

**Improving norms for psychological and educational tests**

The following issues are important for this project:

- For most norms statistics, standard errors are currently not available. Standard errors and confidence intervals based on the standard errors quantify the precision with which the norm statistics have been constructed. Methods and software to derive standard errors of norms from the test data should be made available; these are necessary conditions for investigating the precision of norms. Also, test constructors should report standard errors to demonstrate the precision of the norms. For the sample mean,
*X*, standard errors are available using the well-known formula S(X) = S(X) /√N, but not for almost all other norms. - It must be investigated whether the regression-based norming procedure is robust against violations of the assumptions of the linear regression model. Semel et al. (2004) and Tellegen and Laros (2011) suggested it was not robust, but it was never seriously investigated. Results should indicate the conditions under which regression-based norming produces unbiased results.
- For conditions in which the regression-based norming procedure yields biased results, the norming procedure should be adapted to accommodate those violations. Semel et al. (2004) and Tellegen and Laros (2011) constructed norms using nonlinear regression, but a rigorous justification for this approach is missing and badly needed. Alternatives for regression-based norming must be developed and investigated.
- Whenever a person’s test score is compared to a norm, it is tacitly assumed that the test score is perfectly reliable. This assumption is unrealistic as test scores are always measured with error, so that a test score cannot be taken at face value (Lord & Novick, 1968). Hence, the true, error free test score may correspond to a different percentile, stanine or standard score than the observed test score. A procedure is required that takes measurement error into account, when comparing a test score to norms.

**Financed by
**NWO