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 than 95% confidence, k=2 yields the 96.1% confidence limits 4.6-5.8, and k=1 yields 99.6% confidence limits 4.5-6.2.

Nonparametric statistics make no assumptions about the shape of either the parent population or the data distribution function. Thus nonparametric statistics cannot recognize that any data value is anomalous, and data rejection criteria such as Chauvenet’s criterion are impossible. In a sense, nonparametric statistics are intermediate between rejection of a suspect point and blind application of parametric statistics to the entire dataset; no points are rejected, but the extreme points receive much less weighting than they do when a normal distribution is assumed.

One fast qualitative (‘quick-and-dirty’) test of the suitability of parametric statistics for one’s dataset is to see how similar the mean and median are. If the difference between them is minor in comparison to the size of the standard deviation, then the mean is probably a reasonably good estimate, unbiased by either extreme data values or a strongly non-normal distribution. A rule of thumb might be to suspect non-normality or anomalous extreme values if 4($\overline{X}$-¨X)>σ, where ¨X is the median.