From what I recall, Stanford accepts roughly 1% of applicants to the Computer Science program, compared with just over 10% for the University as a whole, making it one of the most competitive programs in the nation.
That may be true for Ph.D. students, but not for undergraduates. Undergraduate applications are reviewed without regards to major. You'll have an equal chance of getting in whether you express interest in CS or English. The Stanford admissions website confirms this. [1]
The Ph.D. program may have acceptance rates approaching 1%, although I don't really think it's that low. Also, the master's program accepts a significantly higher percentage of applicants than the doctoral program.
[1] "All applicants apply to Stanford through the Office of Undergraduate Admission, not to a particular school or department within the University, and Stanford does not give preference to any major." http://admission.stanford.edu/applying/1_8_faqs.html
You're right, in that I cannot find anyone claiming the significantly lower figure for CS admissions in particular. Even at 10%, it is among the most competitive programs in the country. Both Williams and Amherst, the top two liberal arts colleges in the US, have over 15% admissions, while Yale and Harvard come in usually between 8% and 10%.
On a side note, I have some doubt that the admissions process is truly blind to your stated major of interest. These schools do have a desire to maintain balance between their programs.
They're not blind, but you can also put down anything you want, including "undecided". I was certain I wanted to be a physics major when I applied to college. Things change.
That may be true for Ph.D. students, but not for undergraduates. Undergraduate applications are reviewed without regards to major. You'll have an equal chance of getting in whether you express interest in CS or English. The Stanford admissions website confirms this. [1]
The Ph.D. program may have acceptance rates approaching 1%, although I don't really think it's that low. Also, the master's program accepts a significantly higher percentage of applicants than the doctoral program.
[1] "All applicants apply to Stanford through the Office of Undergraduate Admission, not to a particular school or department within the University, and Stanford does not give preference to any major." http://admission.stanford.edu/applying/1_8_faqs.html