Margin of Error
Definition
Half the width of a symmetric confidence interval, equal to the critical value multiplied by the standard error. Commonly reported in survey and database studies. The full interval is the point estimate plus or minus the margin of error.
- Formula
- Critical value x standard error
- Relation to CI
- Half the width of a symmetric confidence interval
- Common use
- Survey and database studies
- Reported as
- Point estimate plus or minus the margin
Common questions
Why does a smaller margin of error not automatically mean a more trustworthy result?+
The margin only reflects sampling variability at a chosen confidence level; it says nothing about bias from a non-representative sample, measurement error, or an unrepresentative database, so a tight margin around a biased estimate is still a biased estimate.
How does sample size affect the margin of error in forensic database statistics?+
The margin shrinks roughly with the square root of the sample size, so quadrupling the reference sample only halves the margin, which is why forensic frequency estimates from small population databases can carry a wide margin even when the underlying method is sound.
Related terms
- Bayesian Credible Interval
- An interval computed from the posterior distribution of a parameter, given a prior and the observed data. Unlike a confidence interval, a...
- Confidence Interval (CI)
- A range computed from sample data using a procedure that, over many repetitions, would contain the true population parameter a stated percentage...
- Coverage Probability
- The true long-run proportion of intervals, from repeated sampling, that contain the parameter. If a procedure has 95% nominal coverage and its...
- Critical Value
- The value from a reference distribution (z or t) that cuts off the desired tail probability. For a 95% two-sided interval using...
- Standard Error (SE)
- The standard deviation of the sampling distribution of an estimator. For the sample mean, SE equals the population standard deviation divided by...