Student or Learner
This is confusing. I thought "varying"'s subject is "Randy Garner" so I interpreted "while he was varying", but the translation goes "which varied = the surveys varied information". I think suverys is a thing that can't exert an action.
However, either way doesn't make big difference. What do you think?
ex) Randy Garner, of Sam Houston State University, mailed surveys, varying the information on the cover sheet to ensure that the first name of the addressee either matched or didn’t match the experimenter’s first name. So in the “matching name” group, a participant named Fred Smith might receive a survey from researcher Fred Jones, while in the “non-matching name” group, participant Julie Green might get a survey from Amanda White. This remarkably simple manipulation affected the response rate, with 30 percent in the non-matching name condition returning the survey, compared to 56 percent returned from those who saw their own first name on the cover. This work suggests that people are far more likely to support, and agree with, those who appear to be like them.
The survey-taker varied (changed) the information on the cover letter for each recipient.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.