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This means that the confidence level represents the theoretical long-run frequency(i.e., the proportion) of confidence intervals that contain the true value of the unknown population parameter. In other words, 90% of confidence intervals computed at the 90% confidence level contain the parameter, 95% of confidence intervals computed at the 95% confidence level contain the parameter, 99% of confidence intervals computed at the 99% confidence level contain the parameter, etc.[2]
The confidence level is designated before examining the data. Most commonly, a 95% confidence level is used.[3] However, other confidence levels, such as 90% or 99%, are sometimes used. Factors affecting the width of the confidence interval include the size of the sample, the confidence level, and the variability in the sample. A larger sample will tend to produce a better estimate of the population parameter, when all other factors are equal. A higher confidence level will tend to produce a broader confidence interval. Many confidence intervals are of the form (t−cσT,t+cσT){\displaystyle (t-c\sigma _{T},t+c\sigma _{T})}, where t{\displaystyle t}is the realization of the dataset, cis a constant and σT{\displaystyle \sigma _{T}}is the standard deviationof the dataset. [ 1]
Another way to express the form of confidence interval is a set of two parameters: ( point estimate – error bound, point estimate + error bound), or symbolically expressed as (–EBM, +EBM), where (point estimate) serves as an estimate for m(the population mean) and EBM is the error bound for a population mean. [