A Continuous Solution to the Norming Problem

Abstract

Conventional methods for producing test norms are often plagued with "jumps" or "gaps" (i.e., discontinuities) in norm tables and low confidence for assessing extreme scores. We propose a new approach for producing continuous test norms to address these problems that also has the added advantage of not requiring assumptions about the distribution of the raw data: Norm values are established from raw data by modeling the latter ones as a function of both percentile scores and an explanatory variable (e.g., age). The proposed method appears to minimize bias arising from sampling and measurement error, while handling marked deviations from normality-such as are commonplace in clinical samples. In addition to step-by-step instructions in how to apply this method, we demonstrate its advantages over conventional discrete norming procedures using norming data from two different psychometric tests, employing either age norms ( N = 3,555) or grade norms ( N = 1,400).

Keywords: continuous norming; curve fitting; data smoothing; norm generation; norm scores.