Still not a 3:1 ratio. - Edit 1
Before modification by Joel at 06/10/2012 06:09:18 PM
One of my trials came out 69% heads. What I am saying is that this is equivalent to Obama or Romney winning 69 polls out of 100. It is not indicative that the population is bias one way or the other. It still could be random.
Our scenario here, is that we have one trial of 136 polls. Which would be equivalent to 136 coin tosses. You saw a 60% and I saw a 69% so we know that even in a random situation the coin can appear to be biased in a single trial.
The only way to alleviate this problem is by having significantly more coin flips in the trial. As you demonstrated when you added all 500 coin flips together.
Our scenario here, is that we have one trial of 136 polls. Which would be equivalent to 136 coin tosses. You saw a 60% and I saw a 69% so we know that even in a random situation the coin can appear to be biased in a single trial.
The only way to alleviate this problem is by having significantly more coin flips in the trial. As you demonstrated when you added all 500 coin flips together.
It is close, I will give you that, but not quite. And that is the closest either of us got in 10 trials (unless you did the full 10, in which case it is 15.) The same outcome in 69/100 flips once (and 60/100 twice) is thus theoretically possible but very unlikely in 10 (or 15) trials. None our trials showed the same outcome 75/100 times.
Obama leading 75% of 136 polls thus strongly indicates he has (or had) a real advantage. There is a slim possibility the sample is too small to remove all anomalies, but there will always be SOME possibility of that. The probability of it based on the current sample is, however, already quite small (if impossible to know precisely.)