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Calculating Error Ranges

The calculator at the right is designed to compute error ranges around survey percentages automatically. If you would prefer to download a table that will help you do it without the calculator, click here for a printable PDF. Here's some background either way.

Standard Error quantifies the uncertainty that comes from measuring only a sample of a population rather than measuring the whole population. It is determined by two variables:

G&R

Sampling Error Range Calculator  

Enter Confidence Level:

Enter Sample Size:

Enter Observed Percentage:


Click Here to Calculate:   


Margin of Error is:     Calculate!
  1. The sample size (the larger the sample the smaller the
    Standard Error.)

  2. The percentage whose standard error is being calculated (percentages closer to 0 or 100 have smaller Standard Errors.)

Standard Error is used to calculate the range around an observed survey percentage that includes the "real" number that would be obtained if the entire population had been surveyed. This range is usually expressed at a given level of certainty, called the Confidence Level. The Confidence Level states the probability that a given error range includes the "real" population number. In survey research, Confidence Levels of 95%, 90% or 80% are most commonly used. A level of 95% would mean that the "real" population percentage would be included in an error range in at least 95% of the surveys if they were repeated a large number of times. In other words, the odds would be 19 to 1 that the estimate derived from the survey would be correct within the calculated error range. The error range is calculated by multiplying the Standard Error by a constant that is associated with each Confidence Level.

The calculator above does all this for you. Simply enter the desired Confidence Level, the sample size used in your survey and the percentage whose error range you wish to calculate. The resulting error range should be expressed as plus/minus the observed percentage. For example, for a Confidence Level of 90%, a sample size of 500 and a percentage of 60%, the error range would be +/- 3.6% points. That is, if the survey were repeated an infinite number of times, the observed percentage would fall between 56.4% and 63.6% at least 95% of the time. The smaller the error range, the more certain you can be that the survey percentage is correct.

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