ECONOMIC ANALYSES OF WORKING THE REFEREES. Here is a link to a paper by Michael J Lopez published in Economic Inquiry which provides support for the finding that football referees are influenced in making calls by whether they are near a particular team’s sideline.
The paper cites a surprisingly extensive literature applying an economist’s tools to the officiating of athletic events, including over half a dozen papers on pressure on referees to support the home team. Other aspects of refereeing that have been investigated include: changes to the number of referees, their positioning during play, their own previous judgmental decisions, crowd noise, and whether or not a game is televised.
The paper is not a “study” with a small sample. The data included every game during the regular season from 2010 to 2014.
There is a lot of data out there. The study relied on “Armchair Analysis (AA, www .armchairanalysis.com), a website that matches the NFL’s official play-by-play data to game-, team-, and play-specific traits, provided play- and game-specific characteristics for each regular season play between the 2010 and 2014 seasons.”