Margins of Error and Sample Sizes
In case you were wondering about how margins of error are calculated, I put together a handy little graph.
MOE are dependent on only 2 variables: Sample size & the proportional breakdown of respondents. In the middle ranges (say, between 30% & 70%) the differential effects of the proportion itself are relatively negligible. In extreme cases (e.g.95 to 5%), the proportions become important to the calculation. I'm showing 3 curves in the graph, for p=50, 60 and 70%. As you can see these 3 curves are almost identical, leaving sample size as the only important determinant of the MOE. As you look at the graph, you can see that the MOE for a sample size of 100 is about 10, and for 1000, about 3. You have to sample 4,000 people to cut that MOE in half, down to 1.5%. The "sweet spot" chosen by most pollsters is about 1000, for that ± 3% figure. I'm using a 95% confidence interval for the graph, which is what most pollsters use.
(The Y axis is in proportions, not %s, because I was too lazy to convert them in the Excel sheet I used to generate the graph.)
