Recently a question was asked on the NASP listserv on how to find "base rate" information regarding WJ III discrepancy scores. Barb Wendling, a colleague and friend, posted a very thorough response+. I decided to make her well-written explanation below...so it can be readily available for future reference. Kudos to Barb [Conflict of interest statement- I'm a coauthor of the WJ III].
- The conorming of the WJ III ACH and the WJ III COG made it possible to compute discrepancy scores for each individual in the norming sample and then to prepare discrepancy norms using that information. For both the variation and discrepancy procedures, "ACTUAL" discrepancy norms in contrast to "PSEUDO" discrepancy norms are used to determine the significance and frequency of any variations or discrepancies (see report at following link for additional explanation:). These discrepancy norms offer several advantages to practitioners. First, both the cognitive and achievement batteries were normed on the same large, nationally representative sample, eliminating errors from unknown differences that exist when using tests based on different norm samples. Second, the correlation coefficients are known between ability and achievement at all ages so it is not necessary to estimate and make a correction for the amount of regression based on a few correlations and a limited sample. Third, practitioners can evaluate the significance of a discrepancy by using either the percentile rank of the discrepancy (Discrepancy PR) or the difference between the achievement score and the predicted achievement score in standard error of estimate units (Discrepancy SD).
- Discrepancy percentile rank. This score defines the percent of the population that has a particular size discrepancy between the actual and predicted scores. The Discrepancy PR is a norm-based estimate of the BASE RATE of a particular discrepancy in the population. Unlike base rates offered by other tests which are typically based on cross-sectional data, the WJ III provides more precision by reporting the information by subgroups (same age or grade) within the norm sample.
- Discrepancy standard deviation. This score reflects the distance that the examinee’s score is above or below the average score for age or grade mates. The Discrepancy SD allows the criterion of significance to be defined in terms of the standard error of the estimate. Commonly, a Discrepancy SD of +/-1.5 or greater is selected as being significant. A discrepancy of this magnitude would occur approximately 6 out of 100 times. Practitioners may, however, select a different level of significance ranging from +/- 1.0 to +/-2.3 when using the various WJ III software scoring programs.