RyanMaverick said:
But how do you average the scaled scores? I mean your composite is given to you in terms of a percentile, whereas each subsection has you provided with a scaled and a percentile. I was averaging up the percentile averages for each subsection trying to come up with some formula for the composite. It still looks pretty bush-league, perhaps I'm missing something.
It's a pretty complicated system. Scaled scores can range from 200 to 600, with 400 as the stated median score. This seems to suggest that someone scoring 50% correct (missed 20 out of 40, for example) would receive a 400 for their scaled score, while someone who correctly answered 75% of the questions would receive a 500, and a perfect test would result in a 600. However, I have never seen an individual scaled score reach the 500's, and it is hard for me to believe that NO ONE answered even 75% right. I would suggest that the correlation between actual questions missed and scaled score is NOT linear, although I don't know what the correlation is. Let's just assume it's complicated, but that increasing the number of questions you answer correctly also increases your scaled score.
When it comes to percentile scores, Harcourt simply compares your scaled score for the section (however that score was derived) with the scaled scores of test takers from the norm groupall first-time examinees that took the test between October 1998 and March 2003. This comparison results in a percentage. If you got a 92% on the Biology section that means that your scaled score was higher than 92% of the norm group's Biology scaled scores. However, there is usually a range of scaled scores that compose each percentile score - maybe you had a scaled score of 436, your friend had a 434, and your mom had 430 - these could all conceivably correspond to the 92% window.
Composite percentile score simply compares your composite scaled score with that of the norm group's. Your composite scaled score is just the average of the individual sections' scaled scores. So, if you got 479, 430,446,431,and 436 on the individual sections, your composite scaled score would be 444. It is this number that dictates your overall percentile ranking.
So you see, it doesn't really matter what the individual percentile rankings are. As discussed above, you, your friend, and your mom all scored in the 95% for Biology, but your scaled score on that section was a full 6 points higher than your mom's and those points DO matter. Even if you and your mom had the same percentile scores in every sub-section, if you consistently outscored her by a few points in the scaled score, your composite scaled score could be quite a bit higher than her's. When that composite scaled score is compared to the norm group's, you may end up in the 98% range while your mom is in the 94%.
There's actually quite a bit of variation between individual scaled scores and percentile scores, especially if you got a 99% on any individual section. Some people in the 99% literally got every question right, resulting in a very high scaled score. Other people may have missed 7, but still did better than 99% of the norm group. They will have a lower composite scaled score than their perfect counterparts, thus they will probably also have a lower composite percentile score. In other words, your overall percentile score may seem higher than you expected because you totally rocked one or two of the sections.
Sorry for the long post. Hope that helps.
