Gifted Issues Discussion homepage Forums Identification, Testing & Assessment Do Stanford 10 % Ranks Make Statistical Sense?

I get what you're saying, Gusto, and I agree - taken literally (i.e. on the assumption that somewhere there was a sample of children who all took the same tests and percentiles were calculated from them all, no funny weighting) it doesn't make sense. Someone who outscored or equalled your son overall cannot have dropped more than 2 marks in total, so must have outscored or equalled your son in at least one of the two subtests where he dropped a mark (because if someone scores strictly less than him on both of those two, they drop at least 4 marks in total). Therefore, the total number of people who outscore or equal him cannot be larger than the sum of the number of people who outscored or equalled him on those two subtests.

Possibilities other than simple mistakes might include: funny weightings; smoothing/extrapolation; a sample who did not actually all take the same tests. I agree it's weird, and I also agree with all the people who say that this test did not give any kind of ceiling on what your son can do. Welcome!

You are right, of course - 13% same or higher gives 87th percentile. Alternatively, 87% did worse. I was trying to post while extremely tired and in an incredibly distracting environment, and I completely messed up the wording.

The other thing that is confusing people is that composite scores are not "averages" of the scores that went into them. Composites are made by taking the standard scores of the subtests, adding them together, and then treating that as a new raw score which is compared to the raw scores of everyone else in the norming sample. A new standard score and percentile are determined from that.

In general, when all of the scores that go into a composite are in the same direction from the mean (for a gifted kid, typically all above the mean), the composite is *further* from the mean in that direction. That is, if you have subscores of 125, 130, and 135, the composite might very well be 138. Remember that standard scores are measures of "unusualness." It is more unusual to be really good at a lot of things all at the same time than it is to be good at a few things.

With the percentiles, you're seeing, as y'all have noticed, serious ceiling effects, where the item difficulty range was insufficient. Again, the percentile of a composite is not the average of the percentiles of the subtests -- it's the percentile as compared to everyone else's composite "raw score," the same one used to calculate the standard score of the composite. You can also see ceiling effects in standard score norming tables, but you have to be actually looking at the norming tables to know about them.