Wondering if anyone can explain (to a non-mathy person) what the difference is between a national percentile ranking and a normal curve equivalent. I'm looking at score reports for my kids and for DS for math and reading it is 99 across the board for both math and reading NPRs and NCEs, but for DD, the NCE scores are quite a bit lower than the NPRs in both math and reading.

NCEs are another transformation of z scores (standard deviations), just done in such a way that (in a normally-distributed population) a NCE value of 1 = percentile 1, NCE 50 = 50th %ile, and NCE 99 = 99th %ile. Each NCE unit is a fraction of a standard deviation.

Percentiles are an ordinal measure, which describe your ranking in the norm group.

If you have a non-normal distribution of scores, the NCE and percentile will line up even less well.

Ok, so I'm kind of slow with this. I'm assuming that the percentile ranking is more meaningful than the NCE? And what does it mean if they are the same with DS (everything is a 99) but with DD the NCEs are a lot lower (5 to 10 points)? So for instance for math her percentile ranking was 98 (she was unmedicated and her scores dropped a lot), but NCE was more like 90 or 93.

NCEs are just a different measure. Percentiles are really bunched up around the middle of the curve, whereas NCEs are equal-interval measures (based, as they are, on the standard deviation), so they're more spread out than percentiles are in the middle, but closer together than they are at the extremes. That's why out at the tails, a percentile of 98 has a lower NCE. Everything is 99 for DS because NCEs of 99 are defined to be at the 99th %ile. Percentiles are easier for most non-mathy people to understand, as they represent your place in line. The NCE is exactly as meaningful as any other transformation of the standard deviation/z score, such as the standard score used for IQs and achievement tests, or scaled score used for IQ subtest scores. It tells you your distance from the center of the bell curve (defined as NCE = 50). A NCE is like a standard score where the mean = 50, and the standard deviation = about 21.

It's value is that, as an equal-interval scale, it is perceived as being better for making comparisons between different measures, and for measuring growth.

Percentiles can be a bit misleading. If half the class of 31 got 100% then the 16th kid who got 99% would be at about the 50th percentile. The difference in the scores suggests there was something like that going on. When they somehow? Forced the results into a normal distribution some kids went down. They may have added an age rather than grade rating - eg 100% at 7.8 beats 100% at 7.9 etc.

Ok I cross posted. Disregard the second part of the post.

No, puffin, actually NCE 92 or 93 is always going to be 98th %ile, in a normally-distributed population. It isn't a peculiarity of this specific norm group. There will be some oddities comparing NCE to %ile if the data set is not normally-distributed, though.

Although I agree that %iles can be misleading, especially in a tightly-bunched group with outliers. Just like medians. It's just rank-ordering.

Dh majored in math, I'm going to have to show him this thread and make him draw me a picture. Thanks for the explanations.

Here's the picture he'll draw you, blackcat (pdf file).

I go that after I read the post that crossed mine. I just couldn't be bothered deleting the whole thing. I was thinking of something else. Next time i will check the book first. Sorry.

Here's another way of thinking about the NCE: If DD scored a NCE of 92, that's two standard deviations above the mean (50 + 21 + 21), which in standard score terms (like a WISC or WJ score) would be 130, which is at the 98th %ile.

And, obviously, I should have read through your correction to your post, too!

If the normal curve equivalent is reported from the normative data and the national percentile ranking is derived from the current data set, they could be significantly different beyond the mappings that aeh gave.

They are usually derived from the same standardization set. But, of course, that may differ depending on the instrument, and even the school system, as some use local norms for the percentiles. That would be a good place to begin asking questions, in the event that the NCE and %ile do not line up as they would be expected to in a normal distribution.

After looking at the linked visual (thanks!), I understand it now. I'm just not sure how that information is useful. I think they are assuming a normal curve when maybe it's not. Her reading score percentile was 95th and NCE was 85th which matches up with the visual, but maybe in our school district 10 percent of kids are in the top 5th percentile nationally (who knows!). It would be more useful to have THAT info. When they qualify kids for gifted programming they are using national percentile rankings which need to be about 95-98th percentile (depending on the program), but I wonder how many kids from the district fit into that.

blackcat, the NCE is not a percentile, so your DDs NCE is an 85, not the 85th percentile. The NCE score of 85 is mathematically equivalent to the 95th percentile. As aeh stated, the NCE score uses a normal distribution with a mean of 50 and a standard deviation of 21.063. So, an NCE of 85 is 35 points above the mean of 50 (85-50 = 35). Therefore, a score of 85 is 35/21.063 = 1.662 standard deviations above the mean. A standard score of 1.662 standard deviation above the mean of a normal distribution IS the 95.2 percentile. So an NCE of 85 is mathematically equivalent to the 95th percentile. This is the same idea as a WISC score of 125 is equivalent to the 95th percentile (since WISC scores have a mean of 100 and a standard deviation of 15).

Hope this helps and doesn't confuse the matter even more

I understand (and understood when I saw the visual), I shouldn't have said 85th in my last post, just "85" or "a score of 85". At first when I saw that report I thought maybe it meant that she was at the 85th percentile compared to other kids in the district. I think it would be really helpful if they included that info. There is a "district average" on the report but it is on a tiny graph with no actual numbers. District average looks like it's slightly above the national average.

I wonder what the purpose is of providing such confusing information.

The NCE is supposed to facilitate comparisons across instruments and across multiple administrations.

I agree that it often would be more helpful to provide local percentiles, in addition to national percentiles. That's usually an option, sometimes for an additional cost per student record.

FWIW, I think that NCE is also more meaningful than national percentiles, particularly if you are dealing with the tails of the distribution. In a similar sense, that local norm provides far more practical information, especially if it is local to your school rather than the district.