November 06, 2003
Margin Of Error
I follow political polls once in a while, and I finally learned what Margin Of Error (MOE) means.When someone says that Bush has an approval rating of 50% with an MOE of 3.5%, then that always said to me that his approval rating is actually between 46.5% and 53.5%.
But it's not that simple. I didn't know until just now that MOE has to do with a 5% chance. Basically, when there's a margin of error of 3.5%, it means that there is a one in twenty chance that one of the numbers is off by more than 3.5%.
The actual formula is the square root of one over the sample size. So, if I asked 1,000 random people a poll, then the MOE is sqrt(1/1000), or 3.5% .
What I don't know is if the area inside that MOE is a curve. Like, if Bush's approval rating is 50% with an MOE of 3.5%, then is it really most likely 50%? Or is it really just anywhere between 46.5 and 53.5, equally likely among all possibilities?
There are a couple of different things in survey sampling.
-Sample size
-Sample Population
-Confidence Internal (margin of error). Has to be random in order for it be valid.
-Confidence Level
Determining a statistically valid sample is easy enough. The equation to determine sample size is
((1.96^2)*(0.5)*(1-0.5))/(0.05^2)
That is used for a 95% confidence level with a 5+/- confidence interval.
For a 90% confidence level use 1.645 instead of 1.96, for 99% confidence use 2.57.
If the survey sample is a few percent more than the total survey population you are surveying then you also have to make a correction for finite population.
So in your example, if the approval rating was 50% with a +/-3.5% MOE then I would be able to state that we are 95% sure that the true percentage of the population who is in favor of Bush is between 46.5% and 53.5%. We couldn't be as confident that our sample does not contain errors because it was middle of the road 50/50. If however, it was 70/30 we could feel pretty confident that it truly represents the population. I don't get where you are getting that MOE has to do with a 5% chance though?
Oops, for 99%, use 2.576
Posted by: Deborah at November 6, 2003 11:36 PM95% == 19/20.
Oh. :) Well, if you put it like that it could have to do with a 1% chance or a 10% chance too....depending on your confidence level selection.
Posted by: Deborah at November 7, 2003 08:07 AM((1.96^2)*(0.5)*(1-0.5))/(0.05^2)
I understand that 1.96 is a standard figure that is used for +/- 5%... I also see the .05^2 at the end... but what is the .5 and the (1-.5)?
Are these standard figures? I'm not sure where they come from...