1.12:
Uncertainty: Confidence Intervals
Standard deviation provides a measure of nearness between the sample mean and the true mean reliably for a large number of measurements.
So, when there are limited measurements, how is the closeness of the true mean to random data or a sample mean estimated?
A confidence interval is a statistically computed range of values around the mean, in which lies the true mean within a certain probability. The limits of this interval are known as confidence limits.
The confidence limits for the true mean are estimated from the sample's mean, standard deviation, and statistical factor –t–, which depends on the number of measurements and a desired confidence interval.
As the measurements increase, the deviation from the mean becomes small, leading to a narrow confidence interval.
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.