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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

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Answers to Questions (FAQ)

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.

This interval applies to all types of survey / sampling (street interviews, online surveys) in order to evaluate the trust score that can be attributed to it.

The frequency observed in a sample is noted $ f $ and the probability in the total population is noted $ p $, these values are often confused.

How to calculate a confidence interval?

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

With 1.96 the value of the 2.5 percentile of the normal distribution (for 99%, the value will be 2.58).

Example: For a poll with a sample of 80 people of whom 60 declare voting YES, the frequency is $ f = 60/80 $ and the probability $ p = 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[ 0.655, 0.845 \right] $. This means that there is 95% chance in the final vote the YES result is between 65.5% and 84.5%.

How to reduce a confidence interval?

In order to reduce/improve a confidence interval, it is necessary to increase $ N $ (the number of items or people participating in the survey).

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 $ people gives a probability of 0, then the confidence interval is $ [0, 0.03] $, a percentage between 0 and 3%.

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