1.12 : Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or t-score, which depends on the number of degrees of freedom and the desired confidence level. It is important to specify whether a one- or two-tailed confidence interval is needed because the confidence level and the one-tailed t-score table differs from the two-tailed version. As the number of measurements increases, the deviation from the mean decreases, leading to a narrow confidence interval.