I've always had an interest in electrical engineering (actually all engineering in general) and I've decided that I'd like to pursue a graduate degree. I guess I'm wondering if I should really try to do this or just keep it as a fun hobby I spend all my free time doing.
So, the question is, how does one change fields between undergrad and grad school? A specific example follows, but please provide answers that address a more general case, so that your answers will be helpful to other people with the same general question.
I already have a BS and MS in chemistry with a minor in applied math.I published three papers during my MS, one first author in the top journal in my specialty and two as coauthor in an average and a so-so journal. I hope those will count for something. I finished my BS with around 3.1 and my MS with a 3.9 gpa. I'm sure that my MS advisor would write me a great letter. My GRE scores are too old to count so I'd have to retake it or try and get a pass on it since I already have a graduate degree. Since finishing school I've been working for 4 years as a chemist. I can get great recommendations from my supervisor who is a PhD chemist.
I've been working for a while to cover some of the things I would have learned in a BSEE to try and make up for my lack of one. I worked through some texts on analog/digital design, lots and lots of programming, built a balancing robot that got a bit of internet attention, and I'm currently working on an autonomous robotics project that's looking really good so far. After that I have more project ideas than I have time or money for.
I want to apply for PhD programs (specifically in controls/robotics) but I'm worried that my application will get tossed right away because I don't have a BSEE. Maybe I should just apply to MS programs?
I think Dan C has covered the most important points. I will add just one more which is relevant here as the OP mentions to have been a practising chemist for 4 years.
I think professional/industrial experience can also add to the weight of a PhD application. This is even when there may not be any visible or direct connexion between the field being sought for PhD and the field being professed (at or just before the time of the application). Such candidates are desirable because they are assumed to be target-oriented, disciplined, good at time management, and team players.
Therefore, a letter of recommendation from say the director or chief technology officer of the company that highlights such characteristics can also increase one's chances. Actually, if such a letter additionally expresses high confidence on the fast learning and grasping abilities of the candidate (justified with tangible examples along with achievements), then I believe that that letter can be even stronger than letters from your MS co-supervisor or a professor whose lectures you excelled in, etc.