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%. The confidence level represents the probability that the confidence interval constructed from a sample drawn from the population will contain the true value of the parameter. In other words, if we were to sample the population infinite times and construct intervals each time, the proportion of those intervals containing the true parameter value would match the chosen confidence level.

For example, if the estimate for a particular parameter requires a confidence level of 95% with a margin of error of ±5, and if the reported value is 30, then there would be a 95% probability that the true value falls within the range of 25 to 35 (the confidence interval).

In the case of parameters expressed as proportions, the margin of error would be in terms of percentage points, for instance, ±5% points with 95% confidence level. In this case, if the reported value is 30% (e.g., 30 out of 100 respondents said “yes”), then there is a 95% probability that the true value lies within the range of 25% to 35% (the confidence interval).

It is worth noting that the margin of error is often expressed as a proportion or percentage of the true value. In the given examples, if the true value is 30 (30%), the margin of error can be expressed as +5/30 = 16.67% of the parameter value.

Note also that any reference to “margin of error of a survey” is incorrect. Surveys themselves do not have margins of error; it is the parameters being estimated that have margins of error, and these margins are usually associated with specific questions or variables.

The sample design of quantitative research studies is based on the parameters that are central to the study’s objective. For instance, in a product test or a simulated test market, the proportion of people 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 the key parameters of interest.