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Confidence Intervals Data Set Properties
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# Confidence Interval - Desirable Properties for Data Sets

The are three desirable properties of a data set from which a confidence interval is derived. They are:

1) Validity - This is the most important property. Validity implies that the confidence interval calculation derived from the entire data set should hold up, or at least a close approximation to it, when a confidence interval is derived from a smaller subset of the original data set.

2) Invariance - This is the 2nd most important property. Invariance means that different scales or ways of measuring the data set will produce an equivalent confidence interval calculation when applying the confidence interval formula. For example, a 95% confidence interval taken from a data set should produce the same confidence interval as a 95% confidence interval taken of the logarithm of that same data set.

3) Optimality - Optimality implies that the confidence interval has been derived from as much data from the data set as possible. The more data that is used, the shorter should be the confidence interval. The smaller the confidence interval size, the more optimal the confidence interval calculation is. It is optimal to use as much data from the data set as possible when trying to calculate the confidence interval.

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