Does Howard Webb favour Manchester United?

Howard Webb is one of the highest ranked referees in the English Premier League. Since 2005 he has been FIFA-listed, and in 2010 he refereed the FIFA World Cup Final between Spain and the Netherlands. There is a lot of great facts on Howard Webb on the wiki site http://en.wikipedia.org/wiki/Howard_Webb, including a criticisms section, where three incidents where Manchester United seems to be favoured.

But what does three incidents say about a referees overall appearance? Let’s instead look at some stats.

Now, I will consider penalties given. You could look at yellow cards or sending offs, but the criticism is mostly about penalties.  

Looking at the top teams of the last five seasons of the Premier League (2007-08 up until now, todays matches not included) we get following summary statistics (source http://www.statbunker.com/):

Team	M	PF	PA	PF/M	PA/M	(PF-PA)/M
Arsenal	16	1	3	0,0625	0,1875	-0,1250
Chelsea	14	1	2	0,0714	0,1429	-0,0714
Liverpool	18	2	2	0,1111	0,1111	0,0000
Manchester City	14	2	1	0,1429	0,0714	0,0714
Manchester United	23	7	2	0,3043	0,0870	0,2174
Tottenham Hotspur	16	1	3	0,0625	0,1875	-0,1250

Where M=Matches refereed, PF=penalties for and PA=penalties against.

So is 0.2174 significantly higher than the rest of the (PF-PA)/M sample?

If we assume normality of data (I know the sample size actually is too small, but I think that for a bigger sample, data would approach normality), the 95 percent confidence interval for the sample without the Man U=MU (funny!) observation is [-0.1556,  0.0556], and the t-test gives a p-value of 0.002159, strongly indicating that the MU observation has no chance of being the real mean value of Howard Webb’s (PF-PA)/M-population. That is, this short analysis suggests that Howard Webb do favour Manchester United, though it’s a hard accusation. An approved analysis would of course compare above results with results of other referees, to decide if Howard Webb really does favour United.

Now I will enjoy Manchester United-Liverpool with Phil Dowd as referee, and I hope he will favour Liverpool.