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Margin of Error

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

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Margin of Error -

Tag(s) : Statistics

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# Margin of Error

## Survey Margin of Error Calculator

 Confidence Level 95% (Error in 1 out of 20 cases) 99% (Error in 1 out of 100 cases) 90% (Error in 1 out of 10 cases)

### What is a margin of error? (Definition)

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).

### How to calculate a margin of error?

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%.

### How to reduce the margin of error?

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.

### What is confidence level and how to use it?

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 $z = 2.58$.

### What is the difference between a margin of error and a confidence interval?

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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