Poll Simulator

= ·

Tap a term to see what it means, or .

Simulate

Example: in an electorate of 100,000 people, 38.6% vote for candidate A. Each poll interviews 1,000 voters drawn without replacement and publishes a 95% confidence interval. Draw polls and see how many intervals contain the true value. The electorate is split into neighbourhoods of about 500 people; switch the design to draw whole neighbourhoods (clusters) or to split the sample across regions (strata), and see what happens to the coverage when the poll publishes the margin of a simple random sample. The intraclass correlation says how alike neighbours vote.

Population N True proportion P (%) Sample size n Confidence (%) Sampling design Intraclass correlation ρ People per neighbourhood b Polls drawn Seed

Step by step

What each term means

Exact Coverage (C): The share of all possible samples whose confidence interval contains the true value P. It is what "95% confidence" promises, and it is almost never exactly 95%: with 1,000 out of 100,000 voters and P = 38.6%, it is 94.98%. The coverage observed in the simulator fluctuates around it.
Sum over the Hits: Runs only over the counts k whose interval, computed with p̂ = k/n and the standard error estimated by the poll itself, contains P. Since k moves in steps of 1, the range of hits is a set of integers, and the ends lost to rounding make the coverage drift from the nominal level.
Ways to Choose k Voters for A: How many groups of k people can be formed from the K = P·N voters for A. In the simulator, K is the true proportion times the population, rounded.
Ways to Complete the Sample: How many groups of n − k people can be formed from the other N − K voters. Every choice of voters for A pairs with any of these, so the two counts multiply.
All Possible Samples: The number of samples of size n that can be drawn from N people without replacement, all equally likely. With n = 1,000 and N = 100,000, it exceeds 10^2,430. The whole fraction is the hypergeometric distribution, the exact probability that the poll finds k voters for A.