Its the sort of decision that often goes the way of the home side.
Indeed, there is statistical evidence to support your hypothesis. I looked into this years ago and found some UK and US PhD research on it - goodness knows where !
Quick Google brings up
Here
Psychologists call this influence conformity. And you can see how it happens. If 70,000 fans scream for a decision it can reinforce the referee's first impression of an incident. Or it can make them subconsciously decide to get the crowd off their backs by giving them what they want.
And to spice up the discussion : "On the other end of the scale, video evidence – while not to everyone's taste – can help. When the instant-replay challenge was introduced to the NFL in 1999 it led to a 29.4% drop in home advantage. In football the effect could be even greater: because the game is low scoring, one decision – a penalty, red card or offside goal – is more likely to affect the result."
A second cricket example
here
"The findings, published by the Journal of the Royal Statistical Society, come amid renewed debate on whether neutral umpires are still required in Test cricket following the emergence of Decision Review System (DRS)."
A third is UK Football Premiership 2012/13
here
"bias per team home and away games, not just home"
And another football one from 2006
here
"Researchers looking at the fouls awarded in 2,500 Premier League matches in 1996-97 and 2002-03 found the supposedly impartial men in black favour the home side. Worse still for teams considered the underdogs, they are likely to be on the receiving end of some of the poorest decisions — home or away."
And a final football study
here
"It’s official: The referee’s a homer, and ‘Fergie-time’ is a reality"
and talking of homer referees
