English Premier League: Excluding the top four teams, is there evidence of skill?

This randomisation tests whether two variables are correlated. If they are uncorrelated, any permutation of the values for the second variable would be equally likely, so the randomisation shuffles the points for the teams (excluding the top 4 and the teams relegated and promoted).

Click Randomise to shuffle the 2013/14 points between the teams. Click Accumulate and randomise several more times. (Uncheck Animate to speed up the randomisation.)

The correlation for the randomised values is only as far from zero as the actual correlation (r = 0.537) in about 5% of randomisations so there is moderately strong evidence of a difference in skill between teams.

Emphasise the general concepts:

Null hypothesis, H0
The points for the teams in the two seasons are uncorrelated
Alternative hypothesis, HA
There is correlation between the points, implying that the points for a team in 2008/9 are related to those in 2007/8
Test statistic
Correlation coefficient
P-value
Probability of getting such an 'unusual' test statistic if H0 is true
Conclusion
A small p-value gives evidence that H0 is not true.

The data set gives the actual results in the English Premier League at the end of the 2012/13 and 2013/14 seasons.

Each year, the bottom three teams are relegated and three teams are promoted from the league below.