This post is aimed at my fellow Clinical Psychology internship-applicant peers. I know the stress in your lives right now. I'm in the same boat. I describe a simple, nifty approach for mapping the statistical macro-terrain you are walking into with your site list. Hopefully, this approach can shed a little light on the anxiety-generating unknowns where ill-defined stress-generators hide out.
I went through the angst-ridden process of tabulating hours, writing essays, getting reference letters, and selecting sites last year. Following the advice of my mentors (and the little-known but gladly publicized consensus among Canadian internship site directors and directors of clinical training), I decided to defer internship application for a year in order to advance dissertation progress. This has turned out to be a good decision for me so far. Site and program directors emphasize that in addition to total hours, breadth of experience, and quality of essays, a completed dissertation carries a lot of weight in their review of applicants. This was information gleaned from a workshop at the Canadian Psychological Association national convention this past June, and to my fairly confident knowledge, directors on both sides of the internship process (programs and sites) are happy for this important criterion (completed dissertation) to be disseminated.
The focus of this blog entry, however, is to share a brief procedure that I have used to assess where I would stand if I were an average applicant with my given list of sites. Picking the list is a bit of an art for clinical pre-doctoral internship applicants. Too few sites on your list, and you may not even get an interview, let alone get matched. For those reading this unfamiliar with the clinical internship application process, the "Match" is the process whereby students and sites rank each other and are optimally matched, one student to one slot, over all registered North American sites. Too many sites on your list, and the Association of Psychology Postdoctoral and Internship Centres (APPIC) will penalize you with increasing fees-per-application (for more than 15 applications there is a kind of 'diminishing returns' cut-off for likelihood of matching, based on APPIC tracking statistics).
In unfamiliar terrain, map the statistical landscape
It struck me that one way to manage my anxiety about this process was to briefly map the 'statistical territory' I was dealing with in applying to APPIC sites. Apart from my own calibre as an applicant, and the quality of my application, I can tame the landscape a little by looking at a simple map of established likelihoods. That is, likelihood of an internship match given an application is submitted, or of interviews given application, or again of matching given an interview.
I call this approach "Ceteris Paribus", from the Latin expression for "all else being equal". The probabilities that come up are those to be expected for the average quality student applying to a given site. Of course, depending on the homogeneity of the 'competitiveness' factor within your list of sites, the 'average student' from site to site can differ greatly.
The approach is as follows:
1) Generate your site list. Most directors will advise 8-12 applications, for best chance of matching. Programs are keen to have their students match. Because of this, there is pressure, often, to over-apply rather than under-apply. This can sometimes cause a 'glut in the system', however, with students applying where they have no intention of going, not to mention fees, paperwork, and lost administration time for the internship site for these "filler applications". APPIC has a punitive fee structure for applications beyond the 15th to discourage just this sort of thing, and the Association sends out statistical reports indicating that the likelihood of matching does not appreciably increase beyond a 15 site-long list. For a bit of perspective though, especially to fellow Canadians: there are a total of 29 sites in Canada, so there is a lot of overlap and filler if everyone is applying to a full 15 site-long list to Canadian sites only.
2) Compile your relevant site statistics through the APPIC online directory. Usually, the past 3 years of applications, interviews, and 'interns hired' counts are reported directly on the APPIC webpage for a given site. Add these three yearly totals together and your get a 3 yr running total for applications, interviews, and interns hired.
3) Create quotient columns of interest. In a spreadsheet (I use Microsoft Excel), line up your sites, with whatever other information you like (I include available slots relevant to my track, for example. Other bits of information could be salary, total number of positions, and a host of other statistics available on each page. Hours requirements, number of postdocs emerging from the internship program -- there is a long list of possible site-specific statistics of interest). The key calculation is to create a column with a quotient of interns hired per application. You can potentially also calculate interviews granted per application, or also of interns hired per interviews given.
4) Review your probabilities or percentages. You will get a probability or percentage for each quotient you choose to calculate. I will focus on the interns hired per applications quotient, but the principles extend to the likelihood of getting an interview (the matching-likelihood-given-an-interview is a bit trickier, and I won't deal with that in this post). Typically, these probability values will be about .03 to .11 or 3% to 11% chance of matching at any given site (from testing with my own list).
5) Insert an extra 'NOT Matching %' column next to 'Matching %' column. In this case, next to a "Matching %" column, create a "NOT Matching %" column. Program this column with a simple formula of " 1 - (Matching % column letter and row). That is, the complement of your matching likelihood, say of 4%, is your likelihood of NOT matching, or 96% in the case of a 4% chance of matching, for a particular site on one row of your spreadsheet.
6) Calculate the product of all your 'Not Matching %' likelihoods. At the bottom of your list, create a cell that computes the product of all your likelihoods of NOT Matching (this can be done in MS Excel with the "Product() function", similar in syntax to "Sum()" for adding down a column). Each of these values will usually be a high probability (the "one minus [small chance of matching]" or complement of chances of matching at a single given site). They will end up computing in a summary cell at the bottom of your 'NOT Matching %' column your chances of NOT MATCHING ANYWHERE (assuming your application will be the average quality of application in each place you apply -- this is untenable, but it's a starting point. Remember, ceteris paribus).
Don't despair! The way less-than-one fractions work is that multiplying even a high value probability value by another less-than-one probability value creates a smaller and smaller total product, especially the more sites you add to the list. This is where the wisdom of many applications can be seen to operate mathematically. (e.g., three sites with a 90% chance of NOT matching yield a .9 x .9 x .9 chance of NOT matching at any of them, or a 73% (.729) chance of NOT Matching, thus a 27% chance of Matching Somewhere (even though each site only gives you a 10% chance). Of course, at a certain point other factors begin to predominate, and an asypmtote (ceiling) is found, generally at the 15-site long list level.
