A rank subdivision of equivalent score for enhancing neuropsychological test norms

Neuropsychological assessment of cognitive functioning is a crucial part of clinical care: diagnosis, treatment planning, treatment evaluation, research, and prediction of long-term outcomes. The Equivalent Score (ES) method is used to score numerous neuropsychological tests. The ES0 and the ES4 are defined respectively by the outer tolerance limit and the median. The intermediate ESs are commonly calculated using a z-score approach even when the distribution of neuropsychological data is typically non-parametric. To calculate more accurate ESs, we propose that the intermediate ESs need to be calculated based on a non-parametric rank subdivision of the distribution of the adjusted scores.

We make three simulations to explain the differences between the classical z-score approach, the rank-based approach, and the direct subdivision of the dependent variable.

The results show that the rank procedure permits dividing the region between ES0 and ES4 into three areas with the same density. The z-score procedure is quite similar to the direct subdivision of the dependent variable and different from the rank subdivision.

By subdividing intermediate ESs using the rank-subdivision, neuropsychological tests can be scored more accurately, also considering that the two essential points for diagnosis (ES = 0 and ES = 4) remain the same. Future normative data definition should consider the best procedure for scoring with ES.