Margin of Error

[making waves]

The sample size has to have certain characteristics also however.

Just picking 1000 people isn't enough.

You have to have a representative mix of the general population.

To get a truely representative poll in a constituency you would have to find how many people vote in a particular polling booth - take a proportion of those - work out a sequence for calling to doors and stick rigidly to it. You would then have ensure you factor in demographic, social class, age etc. to ensure the sample was representaitve. You have to make sure that you have a mock ballot paper that does not influence the selection in any way and you have to make sure that the person doing the opinion poll does not influence the subject in any way. After that you have a 95% probability od being right within a certain margin of error (depending on the size of the sample). Phone polls way down the list in terms of accuracy.

[YGRIII]

Error in statistics can be caused by many different things. The MoE quoted in newspapers etc only relates to the fact that a sample couldnt possibly reflect 100% accurately on the opinions of any given population. Measurement error and badly worded questions are two more common sources of error. Respondents or people filling in forms on their behalf make mistakes of course(or tell lies).
An example of a badly worded question was the recent P.ie poll that didnt allow former GP voters to switch to FF and vice versa. Also of course we had no way of knowing if the people responding actually had voted FF or GP in 2007.
Polling companies of course will be aware of these pitfalls and act accordingly.

Finally the estimate generated by a poll is important. The 3% MoE for FG say on 40%, means its 95% probable that their real vote is between 37% and 43% approx. It doesnt mean that there is a 6% range around the SF or FF votes which are in the teens. SF, FF and LAB the range is more like +/-2%. For the GP, more like */-1%. The closer to 50% you are the bigger the range in absolute terms. In relative terms the range is the same for all.

[RightWingAnarchist]

To get a truely representative poll in a constituency you would have to find how many people vote in a particular polling booth - take a proportion of those - work out a sequence for calling to doors and stick rigidly to it. You would then have ensure you factor in demographic, social class, age etc. to ensure the sample was representaitve. You have to make sure that you have a mock ballot paper that does not influence the selection in any way and you have to make sure that the person doing the opinion poll does not influence the subject in any way. After that you have a 95% probability od being right within a certain margin of error (depending on the size of the sample). Phone polls way down the list in terms of accuracy.

That's not quite right. You're saying that each polling booth is a sub-population in its own right. Other demographics carry weight as well - age, sex, income, etc. The objective is to get a sample that is not skewed. A completely random sample - put all electors into a drum and pick at random would do. However polling companies realise that they cannot do that and that any other method they use may be skewed (e.g. the response rate from some demographics is different than some others) so they identify the demographics that are considered important and seek random samples within those sub-populations. In theory this is no better than a genuine random sample of the whole population - but it does increase people's confidence because it gets rid of a lot of 'but if's! The confidence interval and confidence levels are a pure mathematical formula based on the population size and the sample size.

[Finbar10]

A fairly easy formula is
100/SquareRoot[sample size] % for margin of error.

So if poll size is 1000, this would give
100/Sqrt[1000] = 100/31.6 = 3.1%
margin of error.

Or for a poll size of 500, this would give
100/Sqrt[500] = 100/22.36 = 4.5%

Easy to remember but very slightly out (should really multiply by 0.98
for 95% confidence levels, but not going to make much difference here,
so I ignore).

The square root in the formula means that doubling the poll size won't halve the error. Instead quadrupling the sample size would halve the margin of error.

As an earlier poster said, the formula would give the worst case margin of error.
This is biggest in the middle (for poll levels of around 50%).
Margin of error is smaller towards both edges.

If you really want to adjust for this, use the following formula
(p here is the percentage we're dealing with)

100/Sqrt[sample size] * Sqrt[4*(1-p/100)*p/100] %

So assuming we want margin of error for a party that's polling
5% with a sample size of 500.

We have:
100/Sqrt[500] * Sqrt[4*(1-5/100)*5/100] %
= 100/22.36 * Sqrt[4 *(1-0.05)*0.05 ] %
= 4.5 * Sqrt[4*0.95*0.05] %
= 4.5 * Sqrt[0.19]
= 4.5 * 0.44 %
= 1.96%

So margin of error does come down away from the middle, but not as much as one might think. So having green party at 5% in a 500 person poll, would still imply a confidence range from about 3% up to 7%.