<p>So using that explanation, I can induct a prescription saying to attend the easiest school you get into.</p>
<p>It’s not that simple. You can also use econometric models to account for differences in informational data using Fixed-Effect (FE) hierarchical regressions, assigning a different FE for each school in your sample. </p>
<p>[Fixed</a> effects model - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Fixed_effects_model]Fixed”>Fixed effects model - Wikipedia)</p>
<p>Say you predict that a 4.0 at CalTech is a true 4.0, but that a 3.5 is somewhere between a 3.5 and 4.0 elsewhere; you can set a FE to account for variability in difference of measures. This would require all schools to disclose their exact distributions, however, which is too time- and energy-consuming.</p>
<p>What people do is use a heuristic (much like all the ones described in psychology and behavioral economics) used to pull information from data. People lump certain schools together and make an inference based on what they know about those subsets of schools (MIT, CalTech = grade hard) and they account for these differences when they compare them with non-group schools (Public = grade easy) and use informal implicit comparisons to tease apart information given some data.</p>
<p>However, this is a much more difficult assumption to make than to merely model simple normal distributions with lawful estimators like my earlier explanation.</p>