How to Compute the Margin of Error
In general parlance, margin of error means an allowance for deviation or error. However, margin of error also has a specific mathematical meaning in a statistical context as a term to describe total sampling error. A margin of error is a confidence interval that expresses the likelihood of the event being repeatable. Most statisticians use a 95 percent confidence interval. Take a poll of 100 eligible voters being asked about a mayoral candidate, for example. A sample size of 100 with a normal distribution will have a margin of error of 10 percent. If 60 of those people say they will vote for the candidate, then the confidence interval can be expressed as -- 60 - 10 percent, 60 + 10 percent -- or, in others words, you can have 95 percent confidence that 50 to 70 percent of the voters will vote for the candidate.
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Instructions
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Determine your sample size. Sample size is the critical value in determining margin of error. Margin of error can be closely approximated by 1/√N, where N equals sample size.
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Calculate the margin of error. For N = 100, you have 1/√100. Simplifying gives you 1/10 or .10. For N = 500, you have 1/√500. Simplifying, you have 1/22.36 or .045.
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Convert the margin of error to a percentage by multiplying by 100. For the sample size of 100 with a margin of error of .10, multiplying .10 X 100 equals a 10 percent margin of error. And for the sample size of 500 with a margin of error of .045, multiplying by 100 gives you a 4.5 percent margin of error.
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Tips & Warnings
You can find tables listing the margin of error for various sample sizes at numerous websites or in statistics textbooks or other references. The formula for determining the exact margin of error using critical value and standard deviation or standard error are also found in the Resources section.
