# Margin of Error

Quantitative Methodology

What is the margin of error in statistics?  It’s about guesses, confidence, and probability.  Guesses over time tend to fall in ranges of values; the ranges help us achieve a degree of confidence; and how confident we are time and again can be described by a percentage of probability.  Margins, like the margins of this page if it were printed, allow us some room for error before the ink spills over onto that mahogany desk.  Margin of error allows us to feel confident a certain percentage of the time within a range of allowable error.

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Good Guess.  Often, you will have to make a decision about some data you have gathered, summarizing something—despite uncertainties about how representative your data is of the full population.  It would be ideal if we could somehow know everything there is to know about every member of every population of study, but it is far more likely we will only have a representative sample—and based on that we have to make a guess.  How confident others are of you, or you are of yourself, is based not on guessing correctly just once, but how often your guesses are close to being right (the probability of being right).  This ability to guess very closely to the ideal again and again creates a confidence interval about the ideal, and how far we allow our guess to be above or below the ideal guess is called the margin of error (Nolan & Heinzen, 2011).

Close Guess.  The margin of error is not just a good guess.  The margin of error is a close guess about the confidence interval at a certain level of probability.  Your confidence interval is a range of possible values, typically some deviation from the mean; for example, if your guess is within 2% above or below the mean that would be a margin of error of 2%.  Let’s say your mean is 42, then your confidence interval would be from 40 (42 – 2) to 44 (42 + 2).  However, you also need to convey the likelihood of this interval over a number of trials, which is usually aimed at 95% of the time. This 95% is your level of confidence.

Explicit Guess.  Now that we know our margin of error is a confidence interval at some level of probability, how do we express it? Your margin of error is a plus-or-minus value above and below the ideal, and a percentage figure.  APA style has a nice succinct format to express it.  Using our example, a margin of error of 2% at a confidence level of 95% would be written: M = 42, 95% CI . Typically we would list the standard deviation as well, but for our purposes we will just list our guess as the mean (average) of our sample population (42), the confidence level as a percent (95%), and the margin of error we are allowing (+-2%), where the first figure in brackets (40) is the lower limit of our interval, and the second figure in brackets (44) is the upper limit.  For more specifics if you are using the APA format, please see chapter 4 “The Mechanics of Style” in the APA style manual (American Psychological Association, 2010).

Summary.  What is the margin of error in statistics?  It’s about guesses, confidence, and probability, and it’s about good guesses, close guesses, and explicit guesses.  Margin of error allows us to feel confident a certain percentage of the time, within a range above or below the ideal guess, represented by a margin we believe is least in error.

References

American Psychological Association. (2010). Publication manual of the American Psychological Association (6th ed., Kindle version). Washington, DC: Author.

Nolan, S. A., & Heinzen, T. E. (2011). Essentials of statistics for the behavioral sciences. New York: Worth Publishers.