How to Calculate Margin of Error Rates
The margin of error rate is a statistical term used to describe the range that the true proportion could fall within. They are common in pre-election polls. For example, a poll may say, "Candidate A has 54 percent and candidate B has 46 percent with a 3 percent margin of error." The margin of error is significant because it shows how close values are statistically. For example, if the margin of error in the earlier example was plus or minus 5 percent, the poll would be unable to predict the winner because the actual results could be 49 for candidate A and 51 for candidate B.
- Difficulty:
- Moderately Easy
Instructions
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1
Calculate the alpha value. Divide the confidence level by 100 and subtract the result from one. For example, if your confidence level was 96 percent, you would divide 96 by 100 and get 0.95, then subtract 0.96 from 1 to get 0.04 for the alpha value. The confidence level is set before you start the experiment and determines how sure you can be that the true percentage lies within your margin of error. For example, if you are using a confidence level of 96 percent, there is a 96 percent probability that the true proportion lies within your margin of error.
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2
Calculate the critical probability by dividing the alpha value by two and subtracting the result from one. For example, if your alpha value is 0.04, you would divide it by two to get 0.02 and then subtract 0.02 from one to get 0.98.
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3
Determine the z-score equivalent to your critical probability using a z-score table or calculator that can be found in a link in Resources. For example, 0.98 would convert to 2.054.
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4
Calculate the standard error by dividing the standard deviation by the square root of the same size. For example, if your poll questioned 1,000 people and had a standard deviation of 0.3, your standard error would be about 0.0095.
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5
Multiply the standard error found in step four by the z-score equivalent found in step three to find your margin of error. For example, if your z-score equivalent was 2.054 your standard error was 0.0095, your margin of error would be about 2 percent.
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