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by ebrenes
2281 days ago
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The SATs have a top score, if it were easy to game you'd find many people would clump at the top. That would make it impossible to normalize that distribution into a bell-shape because they're all clustered into the same bucket with no way of spreading them. OP's point was that the perfect scores remain consistently outside of people's grasp despite the variety of resources available to prep for the exam. I only once managed to hit perfect score and my other best scores were one or two questions off. I had been taking the test since I was 11 (for various extracurricular camps/activities) and prepped multiple times for them. The biggest scores jumps were more closely related with my age and academic achievements than anything else. |
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So the SATs are (almost certainly) 3-pl (actually 2) IRT models. Essentially, it's a multivariate generalised linear mixed model to estimate both question difficulty and participant ability.
Normally, they'll estimate the abilities on the logistic scale, and use the percentile to back transform to a standard normal.
Most people don't cluster at the top because they are a good proxy for g, which is an imaginary statistical construct that we use to explain differences in school outcomes.
So I had a long digression here about the usefulness of penalties for guessing, but it turns out the SATs don't do that anymore, so wth?
(ETS invented IRT, that's why I'm pretty sure).