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Confidence Interval of a Survey

Tool for measuring the upper and lower bounds of the confidence interval attributable to a survey. The 95% or 99% confidence interval makes it possible to better qualify the quality of a survey.

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Confidence Interval of a Survey -

Tag(s) : Statistics

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Confidence Interval of a Survey

Survey Confidence Interval Calculator

 Confidence Level 95% (5% error) 99% (1% error)

Tool for measuring the upper and lower bounds of the confidence interval attributable to a survey. The 95% or 99% confidence interval makes it possible to better qualify the quality of a survey.

What is a confidence interval? (Definition)

Definition: A confidence interval is a lower and upper bound that defines a margin of error for the raw results of a survey. The confidence interval evaluates the quality and accuracy of the estimate obtained with the sample surveyed.

How to calculate a confidence interval?

For a survey of $$N$$ people resulting in the probability $$p$$, then the 95% confidence interval is $$\left[p-1.96\frac{\sqrt{p(1-p)}}{\sqrt n},p+1.96\frac{\sqrt{p(1-p)}}{\sqrt n}\right]$$

With 1.96 the value of the 2.5 percentile of the normal distribution.

Example: For a poll with a sample of 80 people of whom 60 will vote YES, the probability $$p = 60/80 = 0.75$$, the confidence interval is $$\left[0.75-1.96\frac{\sqrt{0.75(1-0.75)}}{\sqrt 80},0.75+1.96\frac{\sqrt{0.75(1-0.75)}}{\sqrt 80}\right] = \left[ , \right]$$. This means that there is 95% chance in the final vote the YES result is between 65.5% and 84.5%.

What is the rule of three?

When the probability is close to 0, the calculation of the confidence interval can lead to probabilities outside the interval $$[0,1]$$ which is impossible. One rule is to use the limit as $$3 / N$$.

Example: A poll of N = 100 person gives a probability of 0, then the confidence interval is $$[0, 0.03]$$