I do not know how to answer your question.

However I would like to offer one caution and one suggestion.

When you design your study, or work from existing data, I suggest that you look for some sort of contextual marker, some measure, if you will, of collegiality.

As an example, consider the case of an academic department with a high degree of collegiality. If they kept verbatim minutes of their faculty meetings, you might expect the transcript to include frequent use of first names when the faculty address one another.

Now, imagine the same faculty some time later, after a bitter fight has broken out following a tenure review, and two factions have formed. If verbatim minutes are still kept, one might expect that many of the faculty would address one another as "Dr." or "Professor". In this case, the formality indicates loss of intimacy and a re-assertion of hierarchy, status, or power-distance index, PDI, to borrow from Hofstede.

Counting experiments based on the frequency of "Dr." might give the opposite sense of what would naturally be expected if one were studying intimacy or partnership first-hand, and might completely overwhelm any gender difference, if that was what you were after.

I'd like to point you to a study with which I am only passingly familiar, that, nevertheless, managed to answer a - to my mind - related question of similar difficulty.

You may wish to question the ethics for use of e-mail spear phishing attacks for the purposes of academic research. I confess to being on the fence in that regard with this study.

Nevertheless, in case you are not already familiar with it, it may be of use of its own right and perhaps the question may be related to yours and the experimental design may be useful to you.

If nothing else, you may wish to write to the authors and see if they can answer your question or possibly collaborate in helping you answer it.

Temporal Distance and Discrimination: An Audit Study in Academia

Katherine L. Milkman, Modupe Akinola, and Dolly Chugh

Psychological Science Online

First, published on May 21, 2012 as

doi:10.1177/0956797611434539

Sincerely,

Mark Frautschi

The environment in which you find yourself is fundamental; where there is prejudice or racism you can expect cacophony, genderism and unusuality

I suggest you have a look at the work of Mari Castañeda and also Andrea O'Reilly

I've heard this about what students call their profs, although I don't know of any specific research on the issue.

The other thing to watch out for it what the person's preference is. I prefer my students to call me by my first name, because I'm not a big fan of hierarchy - I think there are many other ways for them to show respect to me besides using a formal title. I think I'm in the minority, though. But I wonder if there's a sex difference in what profs want their students to call them.

Sex of "dr" or "prof" doesn't matter. It's the brain that counts.

Thank you for the perspectives.  I was unable to find concrete numbers on the frequency with which this disparity occurs.  So we put together a grant proposal to investigate whether the disparity is more than just anecdotal.  Will see if we get funded.

I did research on this exact question at my college.  Many years ago though.  I presented the results at a conference (AWP I'm pretty sure), but didn't publish. 

I had faculty keep a log for two weeks of what titles students used to address them. I can try to dig up the paper if you'd like to see it.  [Men were addressed as Dr. more often, women as Professor.]