In my post on writing job letters for non-academic jobs, I encourage people with academic training to abstract their skills and describe them in terms suited to the job they are applying for. You can further help yourself by not using specific phrases often found in job letters written by academics. As a hiring manager in for-profit, non-academic workplaces, I have read many such letters; here are the phrases that make me not want to hire their writers.
“In my thesis, [title], I argue that…” As I noted in the post about job letters, your thesis is, as such, irrelevant to an employer, but the skills and experience (and, in some cases, the knowledge) you have gained may be relevant. Graduate students often have trouble not focusing on their theses, but its title and other details normally belong on a résumé, not in a job letter. Focusing on the thesis as the unit of meaning and importance is a sign to an employer that you are focusing on the habits and values of your old workplace rather than the one you hope to join.
“As a Ph.D., I…” Especially to a non-academic employer, this phrase suggests you place more importance on the fact of the degree you have than on the skills you have. It’s that you have a Ph.D, not that you are a Ph.D, and you are more than the sum of your Ph.D. training. This phrase also creates the worrisome undertone that you won’t value your future colleagues who do not have that degree. If the job calls for a Ph.D., you don’t need to note that you have one, since you would not apply without one in hand or in sight; that information goes on your résumé.
“My publication, [title], shows…” As with your thesis, the publication per se is not the point; the work is the point. This phrase is marginally better than the thesis phrase, because many publications are peer-reviewed, which some non-academic employers take into account. Normally the way to refer to this is indirectly: “subject-matter experts have recognized my work on [topic (not publication title)], by including it in [peer-reviewed journal issue].”
“I was supervised by [famous faculty member]” This phrase is terrible; the information is usually irrelevant except in a small number of fields, primarily in some social sciences, the bench sciences, and computer science, and then only when you are applying to a job directly related to your field of graduate study. Even in those cases you should phrase it as “As a member of [famous professor]’s research team on [relevant topic]….” Unless you are applying to a job where your supervisor’s work is directly relevant and well known, omit this phrase and focus on the work, because however famous the faculty member is in academics, s/he is almost certainly not that famous where you are applying to work.
“As a winner of [prestigious fellowship],…” Normally this information shows up on your résumé rather than in your job letter, where it absolutely should be. The exception to this general rule is if you have won a competitive, substantial grant in support of your graduate work (a grant in support of a project or fieldwork is substantial; a travel grant to a conference is not). Even then, it should generally be referred to as follows: “My project on [topic] garnered competitive grant support [in the amount of [amount] if unusually large].” You want to show how the work was recognized and thereby you were recognized rather than focusing on yourself as winner.
“I publicize my work through my extensive social-media presence.” Unless the job for which you are applying specifically includes social media as part of its responsibilities, you should research the entity to which you are applying carefully before including this or similar phrases. Some firms control their social media presence carefully, some not at all, and some require permission before posting anything about your work. As a very general rule, recruiting information tends to be fine (“My team is hiring a [position]!”) but project information (“My team is working on [cool new thing not yet public]!”) most often is not. Your social media presence and skills, including ResearchGate and Academia.edu, may be fine, even desirable for your prospective employer, but it is important to find out before you tout how you used those skills.
The point of all this advice is to get you to describe your work in terms relevant to your employer rather than only in terms of its academic importance and recognition. On some occasions, those terms are the same, but not often.