American Research Group, Inc.

Ballot Lead Calculator

Does one candidate really have a lead over the other?

The theoretical margins of error provided for most polls do not take into consideration the sampling error for the difference between two estimates that are derived from the same sample. This sampling error is larger than the margins of error for single estimates. Use this calculator to determine if one candidate has a lead over the other based on the results from a poll at the 95% confidence level.

Enter the ballot numbers for the candidates in the poll and then enter the sample size for the poll. Click on the "Calculate Limits" button to determine the lower and upper limits of the 95% confidence interval for the difference in the ballot numbers.

Candidate A %
Candidate B %
Sample size
Upper limit
Lower limit  
Probability of lead %

If the lower limit is 0 or less (a negative number), there is no significant difference between the ballot numbers for candidates A and B. If the lower limit is greater than 0 (a positive number), there is a significant difference between the ballot numbers.

Also included is the probability of candidate A leading candidate B that is not the result of sampling error. There may not be a significant difference between the ballot numbers at the 95% confidence level, but the probability of an actual lead is calculated.

Other calculators:

Sample Size Calculator, Margin of Error Calculator

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