# Margin of Error

## Definition(s)

• The maximum amount by which a Point Estimate might likely deviate from the true value, typically expressed as “plus or minus” a percentage, with a particular Confidence Level. For example, one might express a Statistical Estimate as “30% of the Documents in the Population are Relevant, plus or minus 3%, with 95% confidence.” This means that the Point Estimate is 30%, the Margin of Error is 3%, the Confidence Interval is 27% to 33%, and the Confidence Level is 95%. Using Gaussian Estimation, the Margin of Error is one-half of the size of the Confidence Interval. It is important to note that when the Margin of Error is expressed as a percentage, it refers to a percentage of the Population, not to a percentage of the Point Estimate. In the current example, if there are one million Documents in the Document Population, the Statistical Estimate may be restated as “300,000 Documents in the Population are Relevant, plus or minus 30,000 Documents, with 95% confidence”; or, alternatively, “between 270,000 and 330,000 Documents in the Population are Relevant, with 95% confidence.” The Margin of Error is commonly misconstrued to be a percentage of the Point Estimate. However, it would be incorrect to interpret the Confidence Interval in this example to mean that “300,000 Documents in the Population are Relevant, plus or minus 9,000 Documents.” The fact that a Margin of Error of “plus or minus 3%” has been achieved is not, by itself, evidence of a precise Statistical Estimate when the Prevalence of Relevant Documents is low. 1
• The likely range in which the true population value will be found. 2

## Notes

1. Maura R. Grossman and Gordon V. Cormack, EDRM page & The Grossman-Cormack Glossary of Technology-Assisted Review, with Foreword by John M. Facciola, U.S. Magistrate Judge2013 Fed. Cts. L. Rev. 7 (January 2013).
2. Herb Roitblat, Predictive Coding Glossary.