Another factor is the norms being used. Depending on the institution, there may be local norms, as well as national norms. Some local norms will result in higher percentiles for the same raw score, and others will result in lower percentiles for the same raw score. Some districts also have older children on average (more holdouts/redshirting). If your friend's daughter is not in the same district, or is reporting local percentiles to you, the gaps may be different.
Also, percentiles are closer together in certain parts of the curve than in others (+/- 1 standard deviation; the middle of the bell curve). For instance, +1 standard deviation, or a SS of 115 for most tests, is the 84th %ile. +2 SD is the 98th %ile. +3 SD is the 99.7th %ile. So from the mean to the first SD, it's 34 %ile points, while from the first to the second SD, it's 14 %ile points, and from the second to the third, it's a mere 1.7 %iles. The same thing holds on the other side of the curve. Standard scores are equally spaced based proportionately to the standard deviation difference, not the percentiles.
A small and relatively insignificant change in standard scores, then, could result in a much larger change in percentiles, if it occurred between the 20th and 80th %iles (or so), than if it occurred outside them. Notice the biggest drop you reported was V, where both the age and grade scores were inside that window.
ETA: CogAt uses a mean of 100 and standard deviation of 16, not 15 like most other tests, but since we're discussing percentiles, the argument is exactly the same.
Last edited by aeh; 02/13/15 11:43 AM.
