# Confidence Level and Confidence Interval

The accuracy of the estimate of a parameter is often defined by two statistics — confidence interval and confidence level. The confidence interval is expressed as a range of values (e.g. 25 to 35) that is likely to contain the population parameter of interest.

A related term, margin of error (e.g. ±5) is half the width (or radius) of a confidence interval.

Confidence intervals are constructed at some specific confidence level, such as 90%, 95% or 99%. In statistic lingo, if a population is sampled infinite times and interval estimates are made on each occasion, the proportion of those intervals that contain the true value of the parameter will match the confidence level.

Example: For a particular parameter, suppose the selected confidence level is 95% and the sample is designed for a margin of error of ±5. If the reported value is 30, in that case the probability that the true value lies within 25 to 35 (confidence interval) is 95% (confidence level).

Or if the parameter of interest is expressed in terms of proportions, the margin of error is ±5% points, and the reported value is 30% (i.e. 30 out of 100 respondents said “yes”), then the probability that the true value lies within 25% to 35% (confidence interval) is 95% (confidence level).

Note: Margin of error is often expressed as a proportion or percentage of the true value. In these examples, if the true value is 30 (30%), the margin of error may be expressed as +5/30 = 16.67% of parameter value.

Analysts sometimes talk of the margin of error of a survey. This is a misconception — surveys do not have margins of error, parameters do, and they are usually tied to questions.

For any research study, the sample design considers the parameters that are central to the study’s objective. For instance, for a product test or a simulated test market, the proportion of people who are likely to try the new product, and the proportion who are likely to repeat buy it. Similarly, for an advertising tracking study, advertising awareness would be one of a few key parameters.

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