The study used a points system to rate clubs for transgressions on the pitch since the start of the Premier League in 1992.
Teams collected 25 points for a red card, five for a yellow card and one for each foul.
The Merseyside club have accumulated 21,211 points in 962 games to top the list while Swindon Town are at the bottom with 486 points, although their tally is calculated after 42 games in the inaugural season which featured 22 teams.
Everton are one of only six teams to have contested every season of the Premier League along with Arsenal, Chelsea, Liverpool, Manchester United and Tottenham Hotspur.
All six teams were in the top ten for total 'dirty' points.
Derby County are the dirtiest team on average with nearly 26 points per game. They also have more yellow cards (2.02) and fouls per game (14.28) than any other team.
Blackburn Rovers' 1998-99 season was the dirtiest in Premier League history as they racked up eight red cards and 80 yellow cards with 725 fouls, while Coventry City had the cleanest campaign in 1993-94 with only 12 yellow cards.
The study also revealed that the overall number of fouls have fallen since the league began and last season saw the fewest dismissals since 1993-94.