95% Confidence Interval Width

The 95% confidence interval is a measure of the extent around the mean value where you are sure (at 95%), according to the data dispersion, that the 'true', hypothetical mean value is. It is a measure of uncertainty of the mean value.

The limits of the 95% confidence interval are defined as . The width of the 95% confidence interval is then .

Some explanations:

• Consider that the population from which the participants of the listening test were drawn has any rating distribution, whether normal or not, with a mean µ and standard deviation s.

• Now draw a sample of N participants, and repeat this M times. The central limit theorem dictates that, when M tends towards infinity, the distribution of the mean of each drawn sample N participants tends towards a normal distribution, with mean µ and standard deviation .

• This allows you to estimate the probability that the rating mean of the population µ be equal to the rating mean m of a given sample:

  

  where -1.96 and 1.96 are the values within which exists 95% of a normal distribution, with mean 0 and standard deviation 1.