187:
As non-parametric methods make fewer assumptions, their applicability is much more general than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric
195:
Non-parametric methods are sometimes considered simpler to use and more robust than parametric methods, even when the assumptions of parametric methods are justified. This is due to their more general nature, which may make them less susceptible to misuse and misunderstanding. Non-parametric methods
95:
Statistical hypotheses concern the behavior of observable random variables.... For example, the hypothesis (a) that a normal distribution has a specified mean and variance is statistical; so is the hypothesis (b) that it has a given mean but unspecified variance; so is the hypothesis (c) that a
99:
It will have been noticed that in the examples (a) and (b) the distribution underlying the observations was taken to be of a certain form (the normal) and the hypothesis was concerned entirely with the value of one or both of its parameters. Such a hypothesis, for obvious reasons, is called
115:. Notwithstanding these distinctions, the statistical literature now commonly applies the label "non-parametric" to test procedures that we have just termed "distribution-free", thereby losing a useful classification.
163:
Non-parametric methods are widely used for studying populations that have a ranked order (such as movie reviews receiving one to five "stars"). The use of non-parametric methods may be necessary when data have a
154:
to grow as necessary to fit the data, but where individual variables still follow parametric distributions and even the process controlling the rate of growth of latent variables follows a parametric distribution.
140:, which is modeling whereby the structure of the relationship between variables is treated non-parametrically, but where nevertheless there may be parametric assumptions about the distribution of model residuals.
196:
can be considered a conservative choice, as they will work even when their assumptions are not met, whereas parametric methods can produce misleading results when their assumptions are violated.
131:
typically assumed to belong to parametric distributions, and assumptions about the types of associations among variables are also made. These techniques include, among others:
931:
96:
distribution is of normal form with both mean and variance unspecified; finally, so is the hypothesis (d) that two unspecified continuous distributions are identical.
107:
Hypothesis (c) was of a different nature, as no parameter values are specified in the statement of the hypothesis; we might reasonably call such a hypothesis
111:. Hypothesis (d) is also non-parametric but, in addition, it does not even specify the underlying form of the distribution and may now be reasonably termed
230:
is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance.
663:"Universal Linear Fit Identification: A Method Independent of Data, Outliers and Noise Distribution Model and Free of Missing or Removed Data Imputation"
494:
Universal Linear Fit
Identification: A Method Independent of Data, Outliers and Noise Distribution Model and Free of Missing or Removed Data Imputation.
53:
involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others:
427:: tests whether, in 2 Ă— 2 contingency tables with a dichotomous trait and matched pairs of subjects, row and column marginal frequencies are equal.
400:
127:
of a model is fixed. Typically, the model grows in size to accommodate the complexity of the data. In these techniques, individual variables
540:
421:
or
Wilcoxon rank sum test: tests whether two samples are drawn from the same distribution, as compared to a given alternative hypothesis.
779:
Bagdonavicius, V., Kruopis, J., Nikulin, M.S. (2011). "Non-parametric tests for complete data", ISTE & WILEY: London & Hoboken.
464:
382:
203:
of non-parametric tests comes at a cost: in cases where a parametric test's assumptions are met, non-parametric tests have less
800:
784:
595:
397:: tests whether a sample is drawn from a given distribution, or whether two samples are drawn from the same distribution.
916:
900:
883:
861:
841:
821:
761:
737:
409:: tests whether a sample is drawn from a given distribution, sensitive to cyclic variations such as day of the week.
207:. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.
921:
293:
26:
of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as is
508:
279:
81:
482:
46:
The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others:
394:
926:
376:
339:
23:
324:
of the variables being assessed. The most frequently used tests include {{columns-list|colwidth=50em|
38:. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated.
833:
648:
488:
333:
269:
251:
241:
62:
476:
328:
321:
247:
136:
189:
550:
436:
282:
classify the unseen instance based on the K points in the training set which are nearest to it.
286:
31:
545:
452:
403:
by ranks: tests whether > 2 independent samples are drawn from the same distribution.
317:
273:
219:
61:, which do not rely on assumptions that the data are drawn from a given parametric family of
35:
27:
851:
674:
645:
Kendall's
Advanced Theory of Statistics: Volume 2A—Classical Inference and the Linear Model
555:
371:
259:
177:
491:: tests whether matched pair samples are drawn from populations with different mean ranks.
8:
345:
255:
678:
888:
705:
662:
661:
Adikaram, K. K. L. B.; Hussein, M. A.; Effenberger, M.; Becker, T. (16 November 2015).
575:
470:
418:
22:
is a type of statistical analysis that makes minimal assumptions about the underlying
896:
879:
857:
837:
817:
796:
780:
757:
733:
710:
692:
591:
461:: tests whether matched pair samples are drawn from distributions with equal medians.
424:
204:
200:
147:
700:
682:
629:
624:
612:
583:
467:: measures statistical dependence between two variables using a monotonic function.
406:
355:
151:
847:
809:
687:
524:
77:
520:
388:
352:
treatments in randomized block designs with 0/1 outcomes have identical effects
449:: detects differentially expressed genes in replicated microarray experiments.
910:
696:
528:
361:
316:
are mathematical procedures for statistical hypothesis testing which, unlike
433:: tests whether two samples are drawn from distributions with equal medians.
714:
485:: tests whether the elements of a sequence are mutually independent/random.
446:
412:
181:
587:
430:
379:: estimates the survival function from lifetime data, modeling censoring
173:
68:
Statistics defined to be a function on a sample, without dependency on a
415:: compares survival distributions of two right-skewed, censored samples.
512:
516:
458:
235:
69:
289:(with a Gaussian kernel) is a nonparametric large-margin classifier.
263:
238:
is a simple nonparametric estimate of a probability distribution.
165:
660:
876:
Handbook of
Parametric and Nonparametric Statistical Procedures
617:
504:
169:
272:
provides efficiency coefficients similar to those obtained by
368:
treatments in randomized block designs have identical effects
342:: estimates the accuracy/sampling distribution of a statistic
336:: tests whether a sample is drawn from a given distribution
443:
values by examining all possible rearrangements of labels.
244:
is another method to estimate a probability distribution.
832:. Kendall's Library of Statistics. Vol. 5. London:
385:: measures statistical dependence between two variables
358:: measures inter-rater agreement for categorical items
479:: tests equality of two distributions by using ranks.
473:: tests equality of variances in two or more samples.
391:: a measure between 0 and 1 of inter-rater agreement.
827:
728:
Conover, W.J. (1999), "Chapter 3.4: The Sign Test",
455:: tests for differences in scale between two groups.
439:: a statistical significance test that yields exact
222:
models in that the model structure is not specified
932:Mathematical and quantitative methods (economics)
793:Nonparametric Statistics: A Step-by-Step Approach
908:
123:involves techniques that do not assume that the
613:"Preliminary testing: The devil of statistics?"
507:(13th century or earlier, use in estimation by
226:but is instead determined from data. The term
867:Hollander M., Wolfe D.A., Chicken E. (2014).
828:Hettmansperger, T. P.; McKean, J. W. (1998).
790:
610:
732:(Third ed.), Wiley, pp. 157–176,
541:CDF-based nonparametric confidence interval
503:Early nonparametric statistics include the
401:Kruskal–Wallis one-way analysis of variance
158:
144:non-parametric hierarchical Bayesian models
30:. Nonparametric statistics can be used for
721:
296:with polynomial probability distributions.
754:Applied Nonparametric Statistical Methods
745:
704:
686:
628:
830:Robust Nonparametric Statistical Methods
210:
756:(Second ed.), Chapman & Hall,
727:
465:Spearman's rank correlation coefficient
172:interpretation, such as when assessing
89:Kendall's Advanced Theory of Statistics
87:The discussion following is taken from
909:
791:Corder, G. W.; Foreman, D. I. (2014).
751:
643:Stuart A., Ord J.K, Arnold S. (1999),
276:without any distributional assumption.
199:The wider applicability and increased
773:
362:Friedman two-way analysis of variance
254:methods have been developed based on
814:Nonparametric Statistical Inference
180:, non-parametric methods result in
13:
812:; Chakraborti, Subhabrata (2003).
730:Practical Nonparametric Statistics
14:
943:
869:Nonparametric Statistical Methods
576:"All of Nonparametric Statistics"
320:, make no assumptions about the
893:All of Nonparametric Statistics
314:inferential statistical methods
654:
637:
630:10.31273/reinvention.v12i2.339
611:Pearce, J; Derrick, B (2019).
604:
568:
146:, such as models based on the
41:
1:
647:, sixth edition, §20.2–20.3 (
340:Statistical bootstrap methods
688:10.1371/journal.pone.0141486
580:Springer Texts in Statistics
150:, which allow the number of
16:Type of statistical analysis
7:
534:
10:
950:
498:
300:
874:Sheskin, David J. (2003)
489:Wilcoxon signed-rank test
437:Pitman's permutation test
322:probability distributions
270:Data envelopment analysis
252:semiparametric regression
242:Kernel density estimation
137:non-parametric regression
63:probability distributions
917:Nonparametric statistics
871:, John Wiley & Sons.
561:
529:Sign test § History
523:(1710) in analyzing the
483:Wald–Wolfowitz runs test
364:by ranks: tests whether
329:Analysis of similarities
248:Nonparametric regression
159:Applications and purpose
20:Nonparametric statistics
810:Gibbons, Jean Dickinson
551:Resampling (statistics)
395:Kolmogorov–Smirnov test
816:, 4th Ed. CRC Press.
287:support vector machine
119:The second meaning of
117:
32:descriptive statistics
922:Statistical inference
588:10.1007/0-387-30623-4
546:Parametric statistics
513:Median § History
334:Anderson–Darling test
318:parametric statistics
274:multivariate analysis
216:Non-parametric models
211:Non-parametric models
178:levels of measurement
93:
80:, which are based on
49:The first meaning of
36:statistical inference
28:parametric statistics
556:Semiparametric model
477:Tukey–Duckworth test
372:Empirical likelihood
752:Sprent, P. (1989),
679:2015PLoSO..1041486A
774:General references
471:Squared ranks test
57:Methods which are
927:Robust statistics
802:978-1-118-84031-3
785:978-1-84821-269-5
597:978-0-387-25145-5
453:Siegel–Tukey test
310:distribution-free
294:method of moments
205:statistical power
188:methods are more
148:Dirichlet process
113:distribution-free
84:of observations.
59:distribution-free
939:
889:Wasserman, Larry
855:
806:
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766:
749:
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673:(11): e0141486.
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641:
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572:
348:: tests whether
152:latent variables
78:Order statistics
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82:ordinal ranking
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5:
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527:at birth (see
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425:McNemar's test
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419:Mann–Whitney U
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306:Non-parametric
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228:non-parametric
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176:. In terms of
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121:non-parametric
109:non-parametric
76:An example is
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901:0-387-25145-6
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884:1-58488-440-1
881:
878:. CRC Press.
877:
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866:
863:
862:0-471-19479-4
859:
853:
849:
845:
843:0-340-54937-8
839:
835:
834:Edward Arnold
831:
826:
823:
822:0-8247-4052-1
819:
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763:0-412-44980-3
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739:0-471-16068-7
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509:Edward Wright
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447:Rank products
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407:Kuiper's test
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383:Kendall's tau
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168:but no clear
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51:nonparametric
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25:
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895:, Springer.
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511:, 1599; see
502:
440:
413:Logrank test
377:Kaplan–Meier
365:
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313:
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227:
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218:differ from
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182:ordinal data
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24:distribution
19:
18:
431:Median test
389:Kendall's W
346:Cochran's Q
174:preferences
42:Definitions
911:Categories
515:) and the
220:parametric
201:robustness
102:parametric
795:. Wiley.
697:1932-6203
517:sign test
459:Sign test
236:histogram
170:numerical
125:structure
70:parameter
891:(2007).
715:26571035
667:PLOS ONE
582:. 2006.
535:See also
264:wavelets
224:a priori
852:1604954
706:4646355
675:Bibcode
499:History
301:Methods
260:splines
256:kernels
166:ranking
899:
882:
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799:
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736:
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649:Arnold
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505:median
262:, and
190:robust
856:also
623:(2).
562:Notes
897:ISBN
880:ISBN
858:ISBN
838:ISBN
818:ISBN
797:ISBN
781:ISBN
758:ISBN
734:ISBN
711:PMID
693:ISSN
592:ISBN
308:(or
292:The
280:KNNs
250:and
701:PMC
683:doi
625:doi
584:doi
531:).
519:by
129:are
34:or
913::
848:MR
846:.
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699:.
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285:A
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234:A
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65:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.