Definition Confidence level

In statistics, the confidence level indicates the probability, with which the estimation of the location of a statistical parameter (e.g. an arithmetic mean) in a sample survey is also true for the population.

When conducting a survey, confidence levels must be established in advance, as the margin of error as well as the necessary scope of the survey depends on them. In surveys, confidence levels of 90/95/99% are frequently used.

If the confidence level was to be established at 95%, a calculated statistical value that was based on a sample, would also be true for the whole population within the established confidence level – with a 95% chance. In other words: the chances are very high that the arithmetic mean (as a statistical value) of a population is exactly within the margins of error which were established for the survey based on a sample.

Conversely, there is a chance that for many times repeated surveys with new samples, in 5 cases out of 100, one would calculate an arithmetic mean which does not fall within in the confidence interval of the population. The result of the survey would indeed be correct for the respondents themselves, but not representative for the surveyed group.

An example:

A survey asked 2,000 Americans over 14 years, whether they were in favor of the smoking ban in restaurants. Overall, 75% of the respondents answered 'yes'. The confidence level for the survey had been set at 95%, the margin of error was set to 2%.

Due to the confidence level, there is a probability of 95%, that the actual percentage of supporters is within a range of 73-77%, i.e. within the confidence interval (=result +/- margin of error). If we were to conduct the survey 100 times, each with 2,000 different participants, 95 times out of 100, the number of supporters would also be within 73-77% - 5 times out of 100, however, less or more people would answer 'yes'.

Please note that the definitions in our statistics encyclopedia are simplified explanations of terms. Our goal is to make the definitions accessible for a broad audience; thus it is possible that some definitions do not adhere entirely to scientific standards.