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Lingo: The term "nonparametric"

Lingo: The term "nonparametric"

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Lingo: The term "nonparametric"

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The term nonparametric is used inconsistently.

Nonparametric method or nonparametric data?

The term nonparametric characterizes an analysis method. A statistical test can be nonparametric or not, although the distinction is not as crisp as you'd guess.

It makes no sense to describe data as being nonparametric, and the phrase "nonparametric data" should never ever be used. The term nonparametric simply does not describe data, or distributions of data. That term should only be used to describe the method used to analyze data.

Which methods are nonparametric?

Methods that analyze ranks are uniformly called nonparametric. These tests are all named after their inventors, including:  Mann-Whitney, Wilcoxon, Kruskal-Wallis, Friedman, and Spearman.

Beyond that, the definition gets slippery.

What about modern statistical methods including randomization, resampling and bootstrapping? These methods do not assume sampling from a Gaussian distribution. But they analyze the actual data,  not the ranks. Are these methods nonparametric?  Wilcox and Manly have each written texts about modern methods, but they do not refer to these methods as "nonparametric". Four texts of nonparametric statistics (by Conover, Gibbons, Lehmann, and Daniel) don't mention randomization, resampling or bootstrapping at all, but the texts by Hollander and Wasserman do.

What about chi-square test, and Fisher's exact test? Are they nonparametric?  Daniel and Gibbons include a chapter on these tests their texts of nonparametric statistics, but Lehmann and Hollander do not.  

What about survival data? Are the methods used to create a survival curve (Kaplan-Meier) and to compare survival curves (logrank or Mantel-Haenszel) nonparametric? Hollander includes survival data in his text of nonparametric statistics, but the other texts of nonparametric statistics don't mention survival data at all. I think everyone would agree that fancier methods of analyzing survival curves (which involve fitting the data to a model) are not nonparametric.

References

W. J. Conover. Practical Nonparametric Statistics (Wiley Series in Probability and Statistics)ISBN:0471160687.

Wayne W. Daniel, Applied Nonparametric Statistics, IBSN:0534919766.

Jean Dickinson Gibbons and Subhabrata Chakraborti, Nonparametric Statistical Inference, Fourth Edition: Revised and Expanded (Statistics: A Series of Textbooks and Monographs), IBSN:0824740521.

Myles Hollander and Douglas A. Wolfe, Nonparametric Statistical Methods, 2nd Edition, IBSN:0471190454.  

Erich L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks, IBSN:013997735X.

Bryan F.J. Manly, Randomization, Bootstrap and Monte Carlo Methods in Biology, Second Edition, IBSN:0412721309.

Larry Wasserman, All of Nonparametric Statistics (Springer Texts in Statistics), IBSN:1441920447.

Rand R. Wilcox, Applying Contemporary Statistical Techniques, IBSN:0127515410.