Proposed reporting standards for percentile norms in neuropsychology: Point and interval estimates of percentile ranks

Programs: Percentile_Norms_Int_Est.exe and Single_PR_PIE.exe

These two programs for PCs accompany the paper: Crawford, J. R., Garthwaite, P. H., and Slick, D.J. (2009). On percentile norms in neuropsychology: Proposed reporting standards and methods for quantifying the uncertainty over the percentile ranks of test scores. The Clinical Neuropsychologist, 27, 1173-1195 .

Norms for neuropsychological test scores are often presented in the form of percentile ranks, particularly when the distribution of raw scores departs markedly from a normal distribution. The principal advantage of presenting scores as percentiles is that, unlike standardized scores (e.g., IQs, T scores etc), they inform us directly how common or uncommon an indidividual's score is in the normative population. It is also commonly argued that percentiles have the advantage of simplicity: their meaning is apparently unequivocal. However, the devil can be in the detail: There are three, mutually exclusive, definitions of a percentile in common use (American Educational Research Association, American Psychological Association, & National Council on Measurement in Education, 1999, p. 179). The three defintions are:

Definition A: The percentage of scores that fall below the score of interest

Definition B: The percentage of scores that fall at or below the score of interest

Definition C: The percentage of scores that fall below the score of interest, where half of those obtaining the score of interest are included in the percentage

The percentile rank of a raw score can vary markedly depending on which definition has been employed (see Table 1 in the above paper for an illustration). We suggest that this is an unsatisfactory state of affairs and propose that neuropsychologists attempt to settle on a single definition. It could be argued that which of the three definitions should fulfill this role is of secondary importance compared to the desirability that one (any one) should prevail over the two others. However, there is a strong case for preferring Definition C (see paper for reasons). A further problem is that, when percentile norms are presented, the defintion employed is often not specified. This constitutes an (avoidable) source of uncertainty when using percentile norms.

A second source of uncertainty stems from the fact that a neuropsychologist wishes to establish the standing of a patient's score in the normative population (not in the sample that happened to be used to establish the norms). This uncertainty over the true percentile rank of a raw score is unavoidable but its effects can be quantified using statistical methods developed in the above paper and implemented in the accompanying computer programs.

The program Percentile_Norms_Int_Est.exe implements the reporting standards for percentile norms proposed in the above paper. It takes a file of frequency data for raw scores and generates a table of raw scores with their corresponding percentile ranks. The point estimates of the percentile ranks are accompanied by 95% interval estimates. These intervals can be calculated using Bayesian or classical statistical methods, as developed in the paper (the two sets of limits exhibit a high degree of onvergence).

A second program, Single_PR_PIE.exe, can be used when all that is required is a point and interval estimate of an individual's percentile rank (the inputs are: the number of persons in the normative or control sampe scoring below the individual, the number obtaining the same score as the individual, and the size of the normative sample).

Click here to download the Percentile_Norms_Int_Est.exe program as an executable, here to download Single_PR_PIE.exe, or here to download BOTH programs as a single zip file.

Your web browser is most probably configured to recognise that the files are executable. If you have any problems (i.e. the browser treats them as text files), hold down the shift key when clicking. If your network does not allow downloads of executables then downloading the zip file is a solution.

Once downloaded, the programs can be run by any of the normal Windows procedures i.e. by clicking on file in File Manager or by placing on desktop etc.

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The author of this software (John R Crawford) and the University of Aberdeen make no representations about the suitability of the software or about any content or information made accessible by the software, for any purpose.

The software is provided 'as is' without express or implied warranties, including warranties of merchantability and fitness for a particular purpose or noninfringement.

The software is provided gratuitously and, accordingly, the author shall not be liable under any theory or any damages suffered by you or any user of the software.

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