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Nonparametric Method

The nonparametric (distribution-free) method makes no assumption about the shape of the population distribution. It only assumes the distribution is continuous. The bounds are order statistics: actual values from the sorted sample. Which order statistics to use is determined from the binomial distribution and does not depend on the population's shape. The Math Details page gives the exact selection rules.

Because the bounds can only move in whole steps from one sorted data value to the next, the interval usually cannot hit the requested confidence exactly. Quantum XL therefore also reports the Attained Confidence, the confidence the returned interval actually achieves.

When to use it

Use the nonparametric method when the data are not well modeled by a normal distribution, or when you prefer not to assume any distribution. The tradeoff is that it usually needs a larger sample to attain a given confidence, and its bounds are limited to observed data values. For small samples the attained confidence can fall well short of the request, which is a signal to collect more data. When normality is reasonable, the Normal Method is usually tighter.

See the Math Details for the exact order-statistic rules and References.