I've learned that when applying to STEM PhD programs in Australia, you are typically required to draft a research proposal for your potential advisor. This differs from North American universities, where a Statement of Purpose (SoP) is usually required.
My question is: What is the difference between a research proposal and a Statement of Purpose? Additionally, are there any examples of a PhD research proposal draft that I could refer to?
I don't have a sample, but the SoP is more general and has a longer perspective than a Research Proposal (RP).
In the US, a student in a doctoral program isn't normally ready to begin research, having only a bachelors, so the SoP gives a more general idea of what the student wants to specialize in, with much less specificity than a research proposal. It should also say something about career goals (IMO). A student here will normally start with classwork and doesn't always have a dissertation advisor at the beginning, but selects one near or after passing qualifying exams (most fields). The purpose is to convince a committee that you have set a direction. They will compare that with the CV, transcripts, and letters of recommendation to determine if the goals are reasonable and achievable.
For students who are starting a program, especially in programs that require a masters, that expects research to begin almost immediately, the RP has to be much more detailed. What problem, specifically, do you wish to attack, or which papers do you think you can extend; things like that. In some fields, a specific hypothesis might be needed along with some words about (general) methodology. This seems to be what you need in Australia and, for example, Germany. Convince the supervisor that you are ready to start on a particular research proposal. Don't be too grandiose. You probably shouldn't attack classic unsolved problems.
There might be places where something less is required in a RP, but probably not as general as a (US) SoP.
