feilmarg

Feilmarg, commonly referred to as the margin of error, is a statistical measure that expresses the range within which the true value of a population parameter is expected to lie, given a particular level of confidence. It reflects uncertainty arising from the use of a sample rather than the entire population and, in some contexts, from measurement imprecision.

For a proportion estimated from a simple random sample, the margin of error can be approximated as z times the square root of p(1 − p)/n, where z corresponds to the chosen confidence level (for example, 1.96 for 95%). For a mean, it is z times the standard deviation divided by the square root of n. In small populations, a finite population correction may be applied.

The margin of error is half the width of the corresponding confidence interval; a larger MOE means a wider interval and less precision.

Factors that influence MOE include sample size, population variability, the confidence level, and the sampling design. Non-sampling errors such as measurement bias, nonresponse, or coverage errors do not generally affect the calculated MOE in the same way, though they can undermine the validity of the estimate.

In practice, MOE is widely used in public opinion polls, market research, and scientific studies to convey precision. It should not be interpreted as a measure of bias, and it assumes that the sampling method and model are appropriate.

Limitations: MOE assumes random sampling and may be misleading if there are systematic errors or complex survey designs; it is an approximation and depends on the estimator and distribution.