|If sample size is:||sampling error* is:|
|3,000 ||+/- 1.8%|
|2,400,000 ||+/- 0.06%|
* "95% of the time (19 out of 20 times), the true proportion in
the population will be within +/- sampling error %"
 Sample size of the Gallup Poll (1936)
 Sample size of the Literary Digest poll (1936)
|A technical note for the technically minded and curious--the sampling errors in the table were calculated under the assumption that the actual proportion = 50% (e.g., for a sample size of 1,000, 50% +/- 3.1%). If the actual proportion is different from 50%, the sampling errors are smaller, in accordance with the binomial formula, where sampling error = (1.96) x sqrt(P*(1-P)/N), where P=proportion in your sample, e.g., proportion voting for Roosevelt in the Literary Digest poll, and N = sample size). For example, if the population proportion is 40% or 60% (a deviation of 10% from the above assumption of 50%), the sampling errors in the table are lower by a factor of 0.98; if the population proportion is 20% or 80%, the sampling errors in the table are lower by a factor of 0.80. You really don't need to know this, but it's here if you want to!|
Example: Let's say that we take a random sample of Canadian voters, and that 50% of the sample support the Liberal party.
|If our sample size is....||Then there is a 95% chance that out of all Canadian|
voters, the percentage supporting the Liberals is...
|50||50% +/- 13.9% (between 36.1% and 63.9%)|
|100||50% +/- 9.8% (between 40.2% and 59.8%)|
|200||50% +/- 6.9% (between 43.1% and 56.9%)|
|3000||50% +/- 1.8% (between 48.2% and 51.8%)|
You can see from this example how the precision of the survey (i.e., reliability) increases with greater sample size. However, remember that reliability does not equal validity. In the case of the Literary Digest poll, the survey researchers had a very precise (highly reliable) but biased (low validity) estimate of the population.