<p>Based on acceptance rates, how competitive are top tier math, physics, econ, and chemistry phD programs? For example, is the acceptance rate of a top tier math or physics phd program lower than the acceptance rate of the undergraduate program at the same school?</p>
<p>In general, around 5-20% for Top 5-10 programs (something like math will usually have a lower acceptance rate than chemistry). If you dig around enough you can probably find the statistics for particular programs. Look at the departments of graduate studies’ websites. To give an example about how competitive math is, UW-Seattle is ranked 27th by US News and their acceptance rate last year was 7.5%; Northwestern is ranked 16th and they accepted 16% last year.</p>
<p>And there’s a big difference in undergrad v. grad admissions. For one, everyone is applying to the same program for grad admissions (ie, similar backgrounds). In undergrad admissions people usually apply to the school in general.</p>
<p>Also, acceptance rates are a very poor indicator of selectivity for programs such as those that you describe. Undergrad applicant pools are much more similar in distribution. That is, the applicant pools of different schools/programs tend to look more alike. Programs of the sort that you mention attract much more informed and highly self-selected applicant pools. Consequently, programs such as clinical psych at mid-tier schools will seem much more selective than pure math programs at elite institutions even though the bar, in an absolute sense, is much higher at the latter.</p>
<p>Chance threads are generally useless, though I understand the motivation. However, for PhD programs chance threads go from useless to absurd. The professors who will be writing your LsOR are about the only people in a reasonable position to give you any informed guidance.</p>