Quick thoughts, before I procrastinate further on this manuscript.
1. I am uncertain as to how broad or specific I should be about my interests, especially if they skew slightly from the immediate direction of the lab/PI. Are interests aligning with use of modalities that the lab/PI works with a paramount consideration?
Methods are important, yes. General research themes are also important. I don't think you need to be terribly specific at this level but you need to be clear about why you're interested in the work (e.g., how it speaks to/builds upon your previous experiences and how it relates to your longer-term goals). If your interests are not in explicit parallel to those of the lab, always use the lab's goals as a starting point, and frame your interests as possible directions or things you could explore within the existing lab framework. Broad strokes are fine, as you do run the risk of scaring people off if they think you're too divergent. I'd have colleagues read at least this part of your statement carefully and provide feedback before you submit.
2. How much of the statement of purpose should directly address research interests/goodness of fit with the lab (word count/1000 word essay, word count/500 word essay would be helpful if possible). Is it advised to make a roughly outlined research proposal? On the other hand, is this not advised?
Demonstrating lab fit is very important-- assuming these are programs with an apprenticeship model-- but you should talk about the program at large (training environment, resources, practica, etc.) and concordance with your broader training goals, as this also goes toward fit. It will depend on how you structure your letter, but generally, 2/3 program 1/3 lab sounds like a reasonable proportion. Again, I think it's a bit much going into specific research plans, and you might shoot yourself in the foot (save this for the interview, if the conversation goes there).
3. There are not a ton of researchers taking grad students that focus on schizophrenia within the realm of clinical psychology v topics like trauma/mood disorders/addiction/anxiety. Do I fudge
my research interests to try to work with my population of interest or do I sacrifice my population of interest to pursue specific research topics that are of interest to me? A mix of both?
As you go through your training, you'll probably find that research questions and methodology are more important than specific populations. So if you find that you have a genuine interest in the work (despite it not being schiz), I'd consider it. This is not fudging, it's simply adapting your interests to maximize your fit and hit rate, and it is common.
