Tool for measuring the margin of error (confidence interval) associated to a survey (and assess its repeatability).

Margin of Error - dCode

Tag(s) : Statistics

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A margin of error is an estimate of a confidence interval statistically limiting the errors in the raw results of a sampling/survey. The margin of error is based on a level of confidence (usually 95% or 99%) to define the value of the quality of the survey (degree of credibility, associated degree of uncertainty, excluding any selection bias).

The formula for the margin of error is $$ ME = z \times \frac{\sigma}{\sqrt{N}} $$ with $ z $ the confidence level, $ \sigma $ the deviation- population type, $ N $ the sample size.

For a survey with $ N $ respondents, a result having received $ f $ responses, (i.e. a probability $ p = f/N $), then the margin of error (standard error) with a confidence level of 95% is $$ \pm 1.96\frac{\sqrt{p(1-p)}}{\sqrt{N}} $$

The value of 1.96 is that of the 2.5 percentile of the normal distribution (for a 99% confidence level, replace with 2.58).

__Example:__ A survey with a sample of 50 people, 30 of whom said they voted `NO`. The probability of the `NO` vote is $ 30/50 = 0.6 $. The margin of error (at 95%) is $ \pm 1.96\frac{\sqrt{0.6(1-0.6)}}{\sqrt{50}} = \pm 6.8 $ (or 13.6%). The interpretation is therefore a margin of error of 13.6% relative to the result of 60%. So, there is a 95% chance that the result `NO` will indeed be between `46.4%` and `73.6%`.

To reduce / improve the margin of error, increase the number of survey participants.

The margin of error formula shows that the margin of error decreases as the sample size increases.

The confidence level is a probability that indicates the reliability of a result.

A common confidence level is 95%, which means that if the study is repeated several times, the results obtained will fall within the calculated margin of error 95% of the time.

For a confidence level of 95%, use the value $ z = 1.96 $.

For a confidence level of 99%, use the value $ z = 2.58 $.

The margin of error is an estimate of the error associated with a result ($ \pm x $ errors or $ \pm x \% $ error).

The confidence interval is the range of values within which the true population value is likely to lie.

The confidence interval is calculated by adding and subtracting the margin of error from the sample result.

__Example:__ If the sample result is 50% with a margin of error of 3%, the confidence interval is the range [47%, 53%].

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Cite as source (bibliography):

*Margin of Error* on dCode.fr [online website], retrieved on 2024-11-05,

margin,error,confidence,interval,survey,sample,95,99,frequency,probability

https://www.dcode.fr/margin-error

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