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Do they not all train students to be researchers, in addition to the other roles, though? My understanding was that even the most balanced programs still prepare students to conduct research, whereas many PsyD programs may give them a "background" in methodology at most.
I thought that I went to a pretty clincally-focused PhD program (most grads go into private practice/hospital jobs), but we still had heavy labwork and most people published a few things during school, and could have applied to research jobs.
As an example, I went to a scientist-practitioner model clinical psych Ph.D. program at a state flagship university. Of the 6 students in my cohort who graduated with me, 2 have pure academic positions (i.e., research focused; grant funded), and 4 of us went primarily clinical positions, though a few of have done some hybrid stuff (e.g., some teaching and research, but as a small part of or adjunct to a mainly clinical job). I spent many years primarily as an administrator, though with some clinical oversight and supervision responsibilities (it's also the setting where my publications came from). The program has since changed to a "Clinical Scientist" model, with a stated goal of preparing students for careers in clinical research.
I recently sat on a "doctoral project" committee for a student from a local FSPS. While he did a decent research project, the standards were much different and less stringent from I experienced myself. Firstly, the research was not done in conjunction with a specific lab. While there was a faculty advisor, it was not a mentor type of thing where the student worked in his lab (as far as I could tell, there were no labs, in the traditional sense of the word). In reviewing the project proposal, I found that I was the only committee member who noted some serious methodological and statistical issues (e.g., main hypothesis was that the null hypothesis was correct). All that said, at least the student did an empirical project (not required).
I am (and have been for a while) in a position where I review applicants for psychologist positions. My procedure for review generally goes a follows:
1) Trash any from the questionable diploma mills/predatory programs/really crappy local FSPS
2) Verify that the candidate is a licensed psychologist in my with a "health services provider." If not, they get tossed. I don't see any licensed-but-not-HSP. I do occasionally get someone licensed as a school-psychologist (MA level credential). They get tossed.
3) Look for RECENT experience doing the work we need them to do. Bonus points for experience with the same tests, ages, dx, etc.
4) Look for weird patterns of professional behaviors (e.g., change jobs every year or two; work in highly variable settings/populations without some unifying "theme")
5) Look for any personal of professional connections, and follow-up if there are some. It's a small world, and if you burnt bridges I might find out.
6) Do a web search. Families and clients will, so I want to know if there's anything questionable out there. I don't care about the occasional party pic, etc., but things like racism, antisemitism, lot's of gun pics, etc., are at the very least MAJOR red flags.
Honestly, if you get that far, we'd probably offer you the job. It's really hard to find applicants with appropriate experience and interest. Things like type of degree (e.g., Ph.D. or Psy.D. don't really come into the equation, though all things equal I'd give a slight edge to a Ph.D. candidate from uni-based program over any candidate from an FSPS). Research experience with a relevant population or topic might favorably augment an applicant with limited applicable clinical experience, but otherwise it's not that big of a deal.