The difference between the right word and the almost right word is the
difference between lightning and a lightning bug. - Mark Twain
What You Shouldn't Do
As I explain below, the article does a good job of illustrating what you should not do: do not, under any circumstances, write out a statement of purpose and then have a computer blindly replace words with longer synonyms taken from the Microsoft Word Thesaurus. A word is not better merely because it is longer - but sometimes a longer word is the better word. Your goal is to communicate, and you should seek to impress with your message and communication skill - not your ability to find really long words and use them poorly.
Problems With Interpreting the Research Article
First of all, I must say that I love the title of the article you linked: "Consequences of Erudite Vernacular Utilized Irrespective
of Necessity: Problems with Using Long Words Needlessly". From a psychological/cognitive perspective, however, it is not sufficient - or even suitable - to use to draw a conclusion on how one might wish to write a statement of purpose.
An excerpt from Experiment 1 I think will help to understand this. Which of these following sentences is best?
1) I desire to go to Graduate School so that I can learn to recognize literature satisfactorily.
2) I want to go to Graduate School so that I can learn to recognize literature well.
3) I want to go to Graduate School so that I can learn to know literature well.
Here's the problem: these sentences, while similar, do not convey the same precise meaning and attitude!
In the first case, the sentence gives the impression that a person wants to "recognize" literature "satisfactorily". This sounds like a person aspires to be able to read something and say, "Ah, this is definitely a kind of literature."
Moreover, they want to be satisfactory at this skill? If a person wrote a letter of reference for you that read, "This student's skills in English Literature were satisfactory" you'd be damned by faint praise! Here, satisfactory sounds an awful lot like "average" or "met minimum expectations".
This is all for an essay to try to get into Stanford - by any measure a competitive school. You don't need to go to Stanford to be satisfactory at a minor skill. Next applicant!
The next sentence is a little better, as a person wants to be able to do something "well". This is a conservative, but still potentially ambitious, way to say that you want to be actually good at something - superior to the average. "Well" and "satisfactory" may be synonyms (and thus how the word was chosen), but they don't have the same precise meanings or connotations in every context.
The final example sentence says that they want to "know literature well." Knowledge is a higher goal than mere recognition. Compare the phrases "I recognize her" with "I know her" and you get the idea - similar meaning, but not at all the same.
The funny thing is, sentence 1 is marked as "highly complex", 2 is "medium-complexity", and 3 is "original" because word length was used as a proxy for complexity. The originals tended to be marked higher than their "more complex" counterparts, but in every case included in the appendix I found the originals were superior to their algorithmically-derived versions.
At least in Experiment 1, the research shows that replacing words blindly with their longer synonyms results in a poorer quality product than that produced by an intelligent human writing a statement of purpose to try to gain admittance to a competitive University.
Before I go on, I wish to point out that this article is good research and interesting, and helps to build the field, and I do not criticize the authors for trying something and reporting their findings; these findings are a step on the road to greater understanding. But this paper alone is not suitable for drawing conclusions.
How You Should Actually Write
In most fields the goal is actual, genuine communication. Most professors and admittance personnel aren't looking to recruit low-quality bullshitters - they surely think they work with enough of such people as it is! So you need to decide what you are: a brilliant bullshitter with an extraordinarily artful grasp of the language and rhetoric, or a genuine communicator. There is a demand for both sets of people (in some fields more than others -cough-), but you need to decide: which extreme are you closer to fitting?
If you choose to showcase your genuine communication skill and interests in your statement of purpose, write it out from the heart first, and then you can go in and agonize a bit more on word choice. Some things will inevitably need to be made simpler, while sometimes a few big-money words will suit just perfectly.
What always dominates an appraisal of writing is the appropriate words. If I say "I'm going to peruse your missive and aggrandize some terminal verbiage" ... those are big words, but they are also supercilious, awkward, and downright poor choices. It would convey the meaning that I am trying to compensate for a lack of actual intelligence and understanding by trying to baffle you with more obscure parts of the lexicon. [Great, now I can't stop doing it...] Or I'm trying to be funny. Or I'm a bit of an ass... thanks in part to the fundamental attribution error, such inappropriate word choices can doom an application.
Get Advice and Feedback
Statistically, only 1 out of 10 people are in the top 10% of ability in written communication skills. Even for those in the top 10, advice and feedback from others on their actual written work is invaluable and there is no perfect substitute. This applies equally to native and non-native speakers - don't stumble in the dark when you can just turn the light on!
Asking someone to review specific word-choice and phrasing is great, and some people have greater editing skills than others so you'll likely need more than one or two pairs of eyes. A good rule of thumb is if someone is willing to spend the time to write a letter of recommendation for you, they are probably willing to spend a little time going over a letter of purpose with you. After all, they wouldn't want their own words to fall on deaf ears, would they?
Career centers, student-employment departments, English tutors/clubs/Professors, and college application workshops are all potentially great sources of help and review, and if you can bring a written draft of your statement with you then the time might prove extremely productive.
As a parting word of advice, I find that busy people who only spend a few minutes with your writing can be very good sources of help on matters like this, because if they can't understand something or don't like the wording in such a quick read the people who actually read your application probably won't either!