Does the relative size of a department indicate quality?

<ol>
<li>What is the correlation coefficient? Is it significant?</li>
<li>What would the correlation be if you simply ranked the colleges by SAT score, and ignored all information about the departments? </li>
</ol>

<p>Is this “departmental ranking” a global ranking of reputation of colleges based on the prominence of the college -is reflected both in the SAT scores of the students while the USNEWS grad school rank is contaminated by halo effects, also from things like SAT score?</p>