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

I don't understand how the Stanford 10 achievement total battery percentile rank statistically "sums" from the component test percentile ranks. My son appeared to score in the 98th percentile in total reading, 99th percentile in total math, aced the rest of the test, but his total battery percentile is only 93rd....all I can tell from this is he is somewhere between 93rd and 99th (I think)...I have had a few stats classes in college/post grad...this doesn't make sense or I am not reading it right. Please help decipher this for me.

In detail, here are my son's 1st Grade Stanford 10 Achievement Test Scores:

Total Reading: 89/90, Nat'l PR-S = 98-9, Nat'l NCE = 93.3
Total Math: 49/50, Nat'l PR-S = 99-9, Nat'l NCE = 99.0
Language: 30/30, Nat'l PR-S = 98-9, Nat'l NCE = 93.2
Spelling: 30/30, Nat'l PR-S = 89-8, Nat'l NCE = 75.8
Environment: 30/30, Nat'l PR-S = 99-9, Nat'l NCE = 99.0
Total Battery: 228/230, Nat'l PR-S = 93-8, Nat'l NCE = 80.9

PR-S = percentile rank-stanine
NCE = normal curve equivalent

The percentiles look like age equivalents and not grade. Is your son older for the grade?

I'm no testing expert but from my stats and testing classes in Psych, percentiles usually show how many children out of 100 achieved the same score as your child. Even though he had all of the spelling correct about 10 or so other kids also did out of 100.

Like kcab said, this test was not difficult enough to show the differing abilities of the children as many were able to score perfectly.

I understand the headroom concept in general (i.e. in particular the spelling percentile)...clearly this is not a great test to differentiate between 93%, 95%, 99% etc....also my son is a normal age for the 1st grade (7 years, 2 months at time of test)....but the juxtaposition of the total battery percentiles against the component percentiles still does not make sense.

Let's take these test percentiles and place them into an example: a hypothetical modified "decathalon", with 5 events, and 100 athletes...my son gets the highest vault, first place in the pole vault (i.e. 99% as he appeared to do in math), then the 2nd place, 2nd longest in the javelin (i.e. 98% as he appeared to do in reading). Let's say the last 3 events are simple pass/fail tests: drink a bottle of gatorade, eat a protein bar, and eat a bowl of wheaties, and that all 100 athletes complete the last 3 events without issue. If you summed up the results of all 5 events, my son's score should still place him no lower than 2nd place (98%) in the total battery of events, right? The percentiles given to me in the Stanford 10 achievement score sheet do not have that same mathematical logic, leading me to assume that either the component percentiles or the total percentile or both are not true percentiles.

I'm not an expert, but I think that his composite PR simply means that 7% of students missed 2 or less problems on the whole test. What you have to keep in mind is that there would be some students who outperformed your son in one area while under-performing in another. His score on the math part was exceptional, but other students may have missed one more on math but zero on reading or another part. Had he only missed the one problem in math, his PR would have had to be much higher.

Obviously, this test is a really poor test at the high end, with way too low of a ceiling. He did fabulously on the test, and with only 2 questions missed you can't argue that. But 7% of students did just as well (or better) than him, so this test alone isn't going to put him into an "exceptional" achievement category. OTOH, if someone is trying to claim that he is NOT exceptional because of this test, they are way off base.

Think about it this way - 2% or so of the children who took this test did as well or better than your child in reading. 1% did as well or better in math. These may be different groups of children - i.e., the children who did as well or better in reading may have done worse in math, and the ones who did better in math may have done worse in reading. 11% of all children did as well or better in spelling. All told, 7% of the children who took the test missed only two questions or less on the total battery - some of them may have missed those two questions in the same subtest, and so scored lower in that subtest than your child.

Sorry to belabor the point, but if only 1% did as well or better in math (i.e. 49/50, missed one or less questions), and 2% did as well or better in reading (i.e. 89/90, missed one or less questions), how could 7% do as well or better overall (i.e. 228/230, missed two or less questions) given my son's perfect scores in the other sections?

All my son's missed questions (two) were in math and reading (one each)....he didn't lose any ground on the other three sections (100% right)...even if every other student aced the remaining three sections, as my son did, it would not let them "catch up" to his 49/50 on math and 89/90 on reading and thus get a 228/230 or higher.

Whether there is full overlap or no overlap between the students outperforming my son on the math and reading subsets, one or both of the math/reading percentiles would need to be lower for my son if the 93% total percentile is right, given his perfect scores in the other sections...the math, reading and total percentiles shown above cannot be correct simultaneously...thus my question as to whether the component or total percentiles (or neither) are correctly calculated.

This could be a more general issue affecting all students' percentile calculations....the only reasonable explanation I can think of is that only higher performing schools had their kids take the other 3 sections, thus the eligible sample for the full battery (as my son took the test) is much lower and much higher accomplished than the samples that took the "core" reading and math sections...otherwise as noted above it does not appear to make sense.

It is very confusing. My daughter got 30 out of 30 correct on a section, yet her NPR-S was 87-7. On another section she also got 30 out of 30 correct on a section, yet her NPR-S was 89-8. Other sections she got 28 out of 30 and her NPR-S was 98-9. So what we're saying is that 87% of 1st graders scored at least 30/30 on the reading section? So that makes answering all the questions correctly less valuable?

This makes absolutely no sense to me. Very confusing.......

No, not quite. In your example, scoring at the 87th percentile with 30/30 correct means about 13% of first graders scored 30/30 on the reading. Percentile ranks indicate what proportion of the norming group had scores that were lower than the test taker. So a percentile rank of 90 means that 90 percent of the norming group scored the same or lower on the test, percentile rank of 50 means that half of the norming group did the same or worse. A score at the 95th percentile is in the top 5% of performance with respect to the norming group.

[My emphasis.] Unless you're making a nice terminological distinction that I'm not understanding, that doesn't quite make sense, aculady. In the case of 30/30 being reported as 87th percentile, it doesn't make sense to say that this means 87% of people scored the same or lower - because obviously 100% of people scored the same or lower! The only interpretation that makes sense in that case is that (100-87)=13% of people scored the same or higher (in this case that's the same as "scored the same" since there is no higher). The whole issue comes from the question of what is done with people who scored exactly the same as the person in question. Your quote above states both possibilities, but they do not give the same result. It's purely a matter of convention which is used, but for coarse measures one has to know, as it can make a big difference in interpretation.