Did the Judge understand margins of error?

I was concerned when I heard the arguments in court yesterday that the TV3 poll had a margin of error of 3.2%, and that this is greater than the difference between the result of 1.6%, 1.4% and 0.4% (being ACT, United and Progressive respectively).

I was even more concerned that the Judge said “It [TV3] had based its decision on a single opinion poll — which expert testimony had said had a margin of error greater than the margins between the smaller parties.”

You see the fundamental mistake is that the 3.2% margin of error is a maximum one which applies for a sample of 1,000 for a result of 50%. It means with 95% confidence the true result is between 46.8% and 53.2%. But if the result is less than 50%, then the margin of error shrinks. This is crucial.

The actual margin of error, and 95% confidence interval for each party is:

ACT 1.6% = 0.8% moe = range of 0.8% to 2.4%

United 1.4% = 0.7% moe = range of 0.7% to 2.1%

Progressive 0.4% = 0.4% moe = range of 0.0% to 0.8%

Now one can also calculate the probability that one party is actually ahead of another party. There is a calculator (excel) linked here.

The probability ACT is ahead of United Future is 64.3%. The probability ACT is ahead of Progressive is 99.7% and probability United is ahead of Progressive is 99.1%.

Therefore any decision to allow Progressive into the debate, on the basis of the margin of error, is highly flawed. There is only a 0.3% chance (at 95% confidence) that they have more support than ACT.

I look forward to seeing the court record (if there is a way to see it) to find out whether it was made clear to the Judge that the 3.2% margin of error quoted had not relevance to the issue. The relevant margins of error range from 0.4% to 0.8%.