English Premier League, 2013/14 — are teams equally-matched?

The examples in this section use simulations to informally perform hypothesis tests. In this example, the null hypothesis is that all teams are equally matched with each match having probs equal to the propns observed overall in the league:

The table on the left is the actual league table. The Simulate button simulates all 380 games in a season and shows the simulated league table on the right.

The standard deviation of points is the test statistic — it will be high if H0 (equally matched teams) is false.

Click Accumulate and simulate the league about 100 times. (Hold down the Simulate button.)

A standard deviation as high as that in the actual league is unlikely for evenly matched teams so there is strong evidence that the top teams are 'better' than the bottom ones.

Emphasise the general concepts:

Null hypothesis, H0
All teams have same probs
Alternative hypothesis, HA
Some teams are better than others (and have higher probs of winning)
Test statistic
Standard deviation of points
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 are the actual results in the English Premier League at the end of the 2008/9 season.