In contrast to point estimators, confidence interval estimate a parameter by specifying a range of possible values.

The interval is linked to a confidence level, which describes the the probability that the sampling procedural will produce an interval containing the true parameter. In other words, a 95% confidence interval means that if we perform the sampling process a bunch of times and work out the confidence interval, we expect 95% of the confidence intervals to contain the true unknown population parameter. confidence interval.png

Computation of the Confidence Intervals

The confidence interval is typically calculated as the point estimate (e.g., sample mean) plus or minus a multiple of the standard error 1:

where is a number coming from the standard normal distribution that corresponds to the desired confidence level. Higher confidence levels result in larger multiples of the standard error, which leads to wider confidence intervals. The relationship between confidence levels and confidence intervals can be understood through the 68-95-99.7 rule. Standard_deviation_diagram.svg

Resources

Footnotes

  1. Standard error and confidence intervals