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Revisi terkini sejak 19 Februari 2024 03.48

Statistika nonparametrik adalah cabang statistika yang tidak hanya didasarkan pada keluarga distribusi probabilitas yang terparameterkan (contoh umum dari parameter adalah mean dan varians). Statistik nonparametrik didasarkan pada distribusi bebas atau memiliki distribusi yang ditentukan tetapi dengan parameter distribusi tidak ditentukan. Statistika nonparametrik mencakup statistika deskriptif dan statistika inferensi.

Definisi

Istilah "statistika nonparametrik" telah didefinisikan atau dimaknai secara umum dalam beberapa cara berbeda. Berikut adalah dua definisi tentang statistik nonparametrik.

Istilah nonparametrik dapat dimaknai sebagai teknik-teknik yang tidak bergantung pada data berasal dari suatu keluarga distribusi yang terparameterkan.^[1] Beberapa metode nonparametrik dalam makna ini adalah:

Metode distribusi bebas (distribution free methods), yang tidak mengasumsikan data diambil (secara spesifik) dari suatu keluarga distribusi probabilitas yang terparameterkan. Metode ini adalah kebalikan dari statistika parametrik.
Statistik nonparametrik, yang membangun suatu statistik sebagai fungsi dari sampel; tanpa ketergantungan pada suatu parameter distribusi. Contoh statistik ini adalah statistik terurut, yang didasarkan pada pengurutan hasil observasi.

Istilah nonparametrik juga dapat dimaknai sebagai teknik-tenik yang tidak mengasumsikan struktur dari suatu model. Umumnya, model akan membesar menyesuaikan kompleksitas dari data. In these techniques, individual variables are typically assumed to belong to parametric distributions, and assumptions about the types of connections among variables are also made. These techniques include, among others:

non-parametric regression, 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.
non-parametric hierarchical Bayesian models, such as models based on the Dirichlet process, which allow the number of latent variables 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.

Aplikasi dan tujuan

Metode nonparametrik banyak digunakan untuk mempelajari populasi yang mengambil urutan peringkat (seperti ulasan film menerima satu hingga empat bintang). Penggunaan metode nonparametrik mungkin diperlukan ketika data memiliki peringkat tetapi tidak ada interpretasi numerik yang jelas, seperti ketika menilai preferensi . Dalam hal tingkat pengukuran, metode non-parametrik menghasilkan data ordinal .

Karena metode non-parametrik membuat asumsi lebih sedikit, penerapannya jauh lebih luas daripada metode parametrik yang sesuai. Secara khusus, mereka dapat diterapkan dalam situasi di mana sedikit yang diketahui tentang aplikasi tersebut. Selain itu, karena ketergantungan pada asumsi yang lebih sedikit, metode non-parametrik lebih kuat .

Pembenaran lain untuk penggunaan metode non-parametrik adalah kesederhanaan. Dalam kasus tertentu, bahkan ketika penggunaan metode parametrik dibenarkan, metode non-parametrik mungkin lebih mudah digunakan. Karena kedua kesederhanaan ini dan keawetannya yang lebih besar, metode non-parametrik dilihat oleh beberapa ahli statistik sebagai menyisakan lebih sedikit ruang untuk penggunaan yang tidak tepat dan kesalahpahaman.

Penerapan yang lebih luas dan peningkatan ketahanan uji non-parametrik dikenakan biaya: jika uji parametrik sesuai, uji non-parametrik memiliki daya yang lebih kecil. Dengan kata lain, ukuran sampel yang lebih besar dapat diminta untuk menarik kesimpulan dengan tingkat kepercayaan yang sama.

Model non parametrik

Model non-parametrik berbeda dari model parametrik karena struktur model tidak ditentukan secara apriori melainkan ditentukan dari data. Istilah non-parametrik tidak dimaksudkan untuk menyiratkan bahwa model seperti itu benar-benar kekurangan parameter tetapi bahwa jumlah dan sifat parameter itu fleksibel dan tidak diperbaiki terlebih dahulu.

Histogram adalah estimasi nonparametrik sederhana dari distribusi probabilitas.
Estimasi kepadatan kernel memberikan estimasi kepadatan yang lebih baik daripada histogram.
Metode regresi nonparametrik dan regresi semiparametrik telah dikembangkan berdasarkan kernel, splines, dan wavelet .
Analisis pembungkus data memberikan koefisien efisiensi yang sama dengan yang diperoleh dengan analisis multivariat tanpa asumsi distribusi.
KNNs mengklasifikasikan instance yang tidak terlihat berdasarkan pada poin K di set pelatihan yang terdekat dengan itu.
Mesin vektor dukungan (dengan kernel Gaussian) adalah classifier margin besar nonparametrik.
Metode momen (statistik) dengan distribusi probabilitas polinomial.

Metode

Metode statistika inferensial non-parametrik (atau bebas distribusi ) adalah prosedur matematika untuk pengujian hipotesis statistik yang, tidak seperti statistika parametrik, tidak membuat asumsi tentang distribusi probabilitas dari variabel yang dinilai. Tes yang paling sering digunakan termasuk

Analysis of similarities
Anderson–Darling test: tests whether a sample is drawn from a given distribution
Statistical bootstrap methods: estimates the accuracy/sampling distribution of a statistic
Cochran's Q: tests whether k treatments in randomized block designs with 0/1 outcomes have identical effects
Cohen's kappa: measures inter-rater agreement for categorical items
Friedman two-way analysis of variance by ranks: tests whether k treatments in randomized block designs have identical effects
Kaplan–Meier: estimates the survival function from lifetime data, modeling censoring
Kendall's tau: measures statistical dependence between two variables
Kendall's W: a measure between 0 and 1 of inter-rater agreement
Kolmogorov–Smirnov test: tests whether a sample is drawn from a given distribution, or whether two samples are drawn from the same distribution
Kruskal–Wallis one-way analysis of variance by ranks: tests whether > 2 independent samples are drawn from the same distribution
Kuiper's test: tests whether a sample is drawn from a given distribution, sensitive to cyclic variations such as day of the week
Logrank test: compares survival distributions of two right-skewed, censored samples
Mann–Whitney U or Wilcoxon rank sum test: tests whether two samples are drawn from the same distribution, as compared to a given alternative hypothesis.
McNemar's test: tests whether, in 2 × 2 contingency tables with a dichotomous trait and matched pairs of subjects, row and column marginal frequencies are equal
Median test: tests whether two samples are drawn from distributions with equal medians
Pitman's permutation test: a statistical significance test that yields exact p values by examining all possible rearrangements of labels
Rank products: detects differentially expressed genes in replicated microarray experiments
Siegel–Tukey test: tests for differences in scale between two groups
Sign test: tests whether matched pair samples are drawn from distributions with equal medians
Spearman's rank correlation coefficient: measures statistical dependence between two variables using a monotonic function
Squared ranks test: tests equality of variances in two or more samples
Tukey–Duckworth test: tests equality of two distributions by using ranks
Wald–Wolfowitz runs test: tests whether the elements of a sequence are mutually independent/random
Wilcoxon signed-rank test: tests whether matched pair samples are drawn from populations with different mean ranks

Sejarah

Statistika nonparametrik awal termasuk median (abad ke-13 atau lebih awal, digunakan dalam estimasi oleh Edward Wright, 1599; lihat Median § History ) dan tes tanda oleh John Arbuthnot (1710) dalam menganalisis rasio jenis kelamin manusia saat lahir (lihat Sign test § History ).^[2]^[3]

Lihat juga

Statistika parametrik
Resampling (statistik)
Interval kepercayaan nonparametrik berbasis CDF
Teori bidang informasi

Catatan

^ Stuart A., Ord J.K, Arnold S. (1999), Kendall's Advanced Theory of Statistics: Volume 2A—Classical Inference and the Linear Model, sixth edition, §20.2–20.3 (Arnold). 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 distribution is of normal form with both mean and variance unspecified; finally, so is the hypothesis (d) that two unspecified continuous distributions are identical. 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 parametric. 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 non-parametric. 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 distribution-free. 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.
^ Conover, W.J. (1999), "Chapter 3.4: The Sign Test", Practical Nonparametric Statistics (edisi ke-Third), Wiley, hlm. 157–176, ISBN 0-471-16068-7
^ Sprent, P. (1989), Applied Nonparametric Statistical Methods (edisi ke-Second), Chapman & Hall, ISBN 0-412-44980-3

Referensi

Bagdonavicius, V., Kruopis, J., Nikulin, MS (2011). "Tes non-parametrik untuk data lengkap", ISTE & WILEY: London & Hoboken. ISBN 978-1-84821-269-5 ISBN 978-1-84821-269-5 .
Corder, G. W.; Foreman, D. I. (2014). Nonparametric Statistics: A Step-by-Step Approach. Wiley. ISBN 978-1118840313.
Gibbons, Jean Dickinson ; Chakraborti, Subhabrata (2003). Inferensi Statistik Nonparametrik, Edisi ke-4 CRC Tekan. ISBN 0-8247-4052-1 ISBN 0-8247-4052-1 .
Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. 5 (edisi ke-First). London: Edward Arnold. ISBN 0-340-54937-8. MR 1604954. juga ISBN 0-471-19479-4 .
Hollander M., Wolfe DA, Chicken E. (2014). Metode Statistik Nonparametrik, John Wiley & Sons.
Sheskin, David J. (2003) Buku Pegangan Prosedur Statistik Parametrik dan Nonparametrik . CRC Tekan. ISBN 1-58488-440-1 ISBN 1-58488-440-1
Wasserman, Larry (2007). Semua Statistik Nonparametrik, Springer. ISBN 0-387-25145-6 ISBN 0-387-25145-6 .

[1] Stuart A., Ord J.K, Arnold S. (1999), Kendall's Advanced Theory of Statistics: Volume 2A—Classical Inference and the Linear Model, sixth edition, §20.2–20.3 (Arnold). 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 distribution is of normal form with both mean and variance unspecified; finally, so is the hypothesis (d) that two unspecified continuous distributions are identical. 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 parametric. 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 non-parametric. 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 distribution-free. 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.

[Conover1999-2] Conover, W.J. (1999), "Chapter 3.4: The Sign Test", Practical Nonparametric Statistics (edisi ke-Third), Wiley, hlm. 157–176, ISBN 0-471-16068-7

[Sprent1989-3] Sprent, P. (1989), Applied Nonparametric Statistical Methods (edisi ke-Second), Chapman & Hall, ISBN 0-412-44980-3

[1]

[2]

[3]

@@ Baris 1: / Baris 1: @@
+[[Berkas:Glu opt.png|jmpl|Contoh estimasi kepadatan bersyarat]]
-'''Statistik nonparametrik''' adalah cabang [[Statistika|statistik]] yang tidak hanya didasarkan pada keluarga parametrized dari [[Sebaran probabilitas|distribusi probabilitas]] (contoh umum dari parameter adalah mean dan varians). Statistik nonparametrik didasarkan pada distribusi bebas atau memiliki distribusi yang ditentukan tetapi dengan parameter distribusi tidak ditentukan. Statistik nonparametrik mencakup statistik [[Statistika deskriptif|deskriptif]] dan [[Statistika inferensi|inferensi statistik]] .
+'''Statistika nonparametrik''' adalah cabang [[statistika]] yang tidak hanya didasarkan pada keluarga [[Sebaran probabilitas|distribusi probabilitas]] yang terparameterkan (contoh umum dari parameter adalah [[Rata-rata|mean]] dan [[varians]]). Statistik nonparametrik didasarkan pada distribusi bebas atau memiliki distribusi yang ditentukan tetapi dengan parameter distribusi tidak ditentukan. Statistika nonparametrik mencakup [[statistika deskriptif]] dan [[statistika inferensi]].
 == Definisi ==
-Istilah "statistik nonparametrik" telah didefinisikan secara tidak tepat dalam dua cara berikut, antara lain. {{Ordered list|The first meaning of ''nonparametric'' covers techniques that do not rely on data belonging to any particular parametric family of probability distributions.
+Istilah "statistika nonparametrik" telah didefinisikan atau dimaknai secara umum dalam beberapa cara berbeda. Berikut adalah dua definisi tentang statistik nonparametrik.
-These include, among others:
-* ''distribution free'' methods, which do not rely on assumptions that the data are drawn from a given parametric family of [[probability distributions]]. As such it is the opposite of [[parametric statistics]].
-* ''nonparametric statistics'' (a [[statistic]] is defined to be a function on a sample; no dependency on a [[parameter]]).
-[[Order statistic]]s, which are based on the [[Ranking#Ordinal ranking ("1234" ranking)|ranks]] of observations, is one example of such statistics.
-The following discussion is taken from ''Kendall's''.<ref>Stuart A., Ord J.K, Arnold S. (1999), ''Kendall's Advanced Theory of Statistics: Volume 2A—Classical Inference and the Linear Model'', sixth edition, §20.2–20.3 ([[Edward Arnold (publisher)|Arnold]]).</ref>
+Istilah ''nonparametrik'' dapat dimaknai sebagai teknik-teknik yang tidak bergantung pada data berasal dari suatu keluarga distribusi yang terparameterkan.<ref>Stuart A., Ord J.K, Arnold S. (1999), ''Kendall's Advanced Theory of Statistics: Volume 2A—Classical Inference and the Linear Model'', sixth edition, §20.2–20.3 ([[Edward Arnold (publisher)|Arnold]]).
-<blockquote>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 distribution is of normal form with both mean and variance unspecified; finally, so is the hypothesis (d) that two unspecified continuous distributions are identical.
+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 distribution is of normal form with both mean and variance unspecified; finally, so is the hypothesis (d) that two unspecified continuous distributions are identical.
 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 ''parametric''.
-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 ''non-parametric''.  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 ''distribution-free''.  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.
+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 ''non-parametric''.  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 ''distribution-free''.  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.</ref> Beberapa metode nonparametrik dalam makna ini adalah:
-</blockquote>|The second meaning of ''non-parametric'' covers techniques that do not assume that the ''structure'' of a model is fixed.  Typically, the model grows in size to accommodate the complexity of the data.  In these techniques, individual variables ''are'' typically assumed to belong to parametric distributions, and assumptions about the types of connections among variables are also made.  These techniques include, among others:
+* Metode distribusi bebas (''distribution free methods''), yang tidak mengasumsikan data diambil (secara spesifik) dari suatu keluarga [[distribusi probabilitas]] yang terparameterkan. Metode ini adalah kebalikan dari [[statistika parametrik]].
-* ''[[nonparametric regression|non-parametric regression]]'', 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.
+* Statistik nonparametrik, yang membangun suatu [[statistik]] sebagai fungsi dari sampel; tanpa ketergantungan pada suatu parameter distribusi. Contoh statistik ini adalah [[statistik terurut]], yang didasarkan pada pengurutan hasil observasi.
-* ''non-parametric hierarchical Bayesian models'', such as models based on the [[Dirichlet process]], which allow the number of [[latent variables]] 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.}}
+Istilah ''nonparametrik'' juga dapat dimaknai sebagai teknik-tenik yang tidak mengasumsikan ''struktur'' dari suatu model. Umumnya, model akan membesar menyesuaikan kompleksitas dari data. In these techniques, individual variables ''are'' typically assumed to belong to parametric distributions, and assumptions about the types of connections among variables are also made.  These techniques include, among others:
+* ''[[Nonparametric regression|non-parametric regression]]'', 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.
+* ''non-parametric hierarchical Bayesian models'', such as models based on the [[Dirichlet process]], which allow the number of [[latent variables]] 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.
 == Aplikasi dan tujuan ==
-Metode non-parametrik banyak digunakan untuk mempelajari populasi yang mengambil urutan peringkat (seperti ulasan film menerima satu hingga empat bintang). Penggunaan metode non-parametrik mungkin diperlukan ketika data memiliki peringkat tetapi tidak ada interpretasi [[Bilangan|numerik yang]] jelas, seperti ketika menilai [[preferensi]] . Dalam hal [[Tipe skala pengukuran|tingkat pengukuran]], metode non-parametrik menghasilkan data ordinal .
+Metode nonparametrik banyak digunakan untuk mempelajari populasi yang mengambil urutan peringkat (seperti ulasan film menerima satu hingga empat bintang). Penggunaan metode nonparametrik mungkin diperlukan ketika data memiliki peringkat tetapi tidak ada interpretasi [[Bilangan|numerik yang]] jelas, seperti ketika menilai [[preferensi]] . Dalam hal [[Tipe skala pengukuran|tingkat pengukuran]], metode non-parametrik menghasilkan data ordinal .
 Karena metode non-parametrik membuat asumsi lebih sedikit, penerapannya jauh lebih luas daripada metode parametrik yang sesuai. Secara khusus, mereka dapat diterapkan dalam situasi di mana sedikit yang diketahui tentang aplikasi tersebut. Selain itu, karena ketergantungan pada asumsi yang lebih sedikit, metode non-parametrik lebih kuat .
@@ Baris 32: / Baris 35: @@
 * [[Histogram]] adalah estimasi nonparametrik sederhana dari distribusi probabilitas.
 * Estimasi kepadatan kernel memberikan estimasi kepadatan yang lebih baik daripada histogram.
-* Metode regresi nonparametrik dan regresi semiparametrik telah dikembangkan berdasarkan kernel , splines , dan [[wavelet]] .
+* Metode regresi nonparametrik dan regresi semiparametrik telah dikembangkan berdasarkan kernel, splines, dan [[wavelet]] .
 * Analisis pembungkus data memberikan koefisien efisiensi yang sama dengan yang diperoleh dengan analisis multivariat tanpa asumsi distribusi.
 * [[KNN]]s mengklasifikasikan instance yang tidak terlihat berdasarkan pada poin K di set pelatihan yang terdekat dengan itu.
@@ Baris 39: / Baris 42: @@
 == Metode ==
-'''Metode statistik inferensial''' '''non-parametrik''' (atau '''bebas distribusi''' ) adalah prosedur matematika untuk pengujian hipotesis statistik yang, tidak seperti statistik parametrik , tidak membuat asumsi tentang [[Sebaran probabilitas|distribusi probabilitas]] dari variabel yang dinilai. Tes yang paling sering digunakan termasuk {{Daftar-kolom|* [[Analysis of similarities]]
+'''Metode statistika inferensial''' '''non-parametrik''' (atau '''bebas distribusi''' ) adalah prosedur matematika untuk pengujian [[hipotesis]] statistik yang, tidak seperti statistika parametrik, tidak membuat asumsi tentang [[Sebaran probabilitas|distribusi probabilitas]] dari variabel yang dinilai. Tes yang paling sering digunakan termasuk
+* [[Analysis of similarities]]
 * [[Anderson–Darling test]]: tests whether a sample is drawn from a given distribution
 * [[Bootstrapping (statistics)|Statistical bootstrap methods]]: estimates the accuracy/sampling distribution of a statistic
@@ Baris 63: / Baris 68: @@
 * [[Tukey–Duckworth test]]: tests equality of two distributions by using ranks
 * [[Wald–Wolfowitz runs test]]: tests whether the elements of a sequence are mutually independent/random
-* [[Wilcoxon signed-rank test]]: tests whether matched pair samples are drawn from populations with different mean ranks|colwidth=50em}}
+* [[Wilcoxon signed-rank test]]: tests whether matched pair samples are drawn from populations with different mean ranks
 == Sejarah ==
-Statistik nonparametrik awal termasuk [[median]] (abad ke-13 atau lebih awal, digunakan dalam estimasi oleh Edward Wright , 1599; lihat {{Section link|Median|History}} ) dan tes tanda oleh John Arbuthnot (1710) dalam menganalisis [[rasio jenis kelamin manusia]] saat lahir (lihat {{Section link|Sign test|History}} ). <ref name="Conover1999">{{Citation|last=Conover|first=W.J.|title=Practical Nonparametric Statistics|edition=Third|year=1999|publisher=Wiley|isbn=0-471-16068-7|pages=157–176|chapter=Chapter 3.4: The Sign Test}}</ref> <ref name="Sprent1989">{{Citation|last=Sprent|first=P.|title=Applied Nonparametric Statistical Methods|edition=Second|year=1989|publisher=Chapman & Hall|isbn=0-412-44980-3}}</ref>
+Statistika nonparametrik awal termasuk [[median]] (abad ke-13 atau lebih awal, digunakan dalam estimasi oleh Edward Wright, 1599; lihat {{Section link|Median|History}} ) dan tes tanda oleh John Arbuthnot (1710) dalam menganalisis [[rasio jenis kelamin manusia]] saat lahir (lihat {{Section link|Sign test|History}} ).<ref name="Conover1999">{{Citation|last=Conover|first=W.J.|title=Practical Nonparametric Statistics|edition=Third|year=1999|publisher=Wiley|isbn=0-471-16068-7|pages=157–176|chapter=Chapter 3.4: The Sign Test}}</ref><ref name="Sprent1989">{{Citation|last=Sprent|first=P.|title=Applied Nonparametric Statistical Methods|edition=Second|year=1989|publisher=Chapman & Hall|isbn=0-412-44980-3}}</ref>
 == Lihat juga ==
-* Statistik parametrik
+* [[Statistika parametrik]]
 * Resampling (statistik)
 * Interval kepercayaan nonparametrik berbasis CDF
@@ Baris 76: / Baris 81: @@
 == Catatan ==
+{{reflist}}
-<references group="" responsive=""></references>
 == Referensi ==
@@ Baris 82: / Baris 87: @@
 * Bagdonavicius, V., Kruopis, J., Nikulin, MS (2011). "Tes non-parametrik untuk data lengkap", ISTE & WILEY: London & Hoboken. {{ISBN|978-1-84821-269-5}} [[International Standard Book Number|ISBN]] &nbsp; [[Istimewa:BookSources/978-1-84821-269-5|978-1-84821-269-5]] .
 * {{Cite book|last=Corder|first=G. W.|last2=Foreman|first2=D. I.|year=2014|title=Nonparametric Statistics: A Step-by-Step Approach|location=|publisher=Wiley|isbn=978-1118840313}}
-* Gibbons, Jean Dickinson ; Chakraborti, Subhabrata (2003). ''Inferensi Statistik Nonparametrik'' , ''Edisi'' ke-4 CRC Tekan. {{ISBN|0-8247-4052-1}} [[International Standard Book Number|ISBN]] &nbsp; [[Istimewa:BookSources/0-8247-4052-1|0-8247-4052-1]] .
+* Gibbons, Jean Dickinson ; Chakraborti, Subhabrata (2003). ''Inferensi Statistik Nonparametrik'', ''Edisi'' ke-4 CRC Tekan. {{ISBN|0-8247-4052-1}} [[International Standard Book Number|ISBN]] &nbsp; [[Istimewa:BookSources/0-8247-4052-1|0-8247-4052-1]] .
 * {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} {{Cite book|last=Hettmansperger|first=T.&nbsp;P.|last2=McKean|first2=J.&nbsp;W.|title=Robust Nonparametric Statistical Methods|edition=First|series=Kendall's Library of Statistics|volume=5|publisher=[[Edward Arnold (publisher)|Edward Arnold]]|location=London|year=1998|isbn=0-340-54937-8|mr=1604954}} juga {{ISBN|0-471-19479-4}} .
-* Hollander M., Wolfe DA, Chicken E. (2014). ''Metode Statistik Nonparametrik'' , John Wiley & Sons.
+* Hollander M., Wolfe DA, Chicken E. (2014). ''Metode Statistik Nonparametrik'', John Wiley & Sons.
 * Sheskin, David J. (2003) ''Buku Pegangan Prosedur Statistik Parametrik dan Nonparametrik'' . CRC Tekan. {{ISBN|1-58488-440-1}} [[International Standard Book Number|ISBN]] &nbsp; [[Istimewa:BookSources/1-58488-440-1|1-58488-440-1]]
-* Wasserman, Larry (2007). ''Semua Statistik Nonparametrik'' , Springer. {{ISBN|0-387-25145-6}} [[International Standard Book Number|ISBN]] &nbsp; [[Istimewa:BookSources/0-387-25145-6|0-387-25145-6]] .
+* Wasserman, Larry (2007). ''Semua Statistik Nonparametrik'', Springer. {{ISBN|0-387-25145-6}} [[International Standard Book Number|ISBN]] &nbsp; [[Istimewa:BookSources/0-387-25145-6|0-387-25145-6]] .
 [[Kategori:Metode matematis dan kuantitatif (ekonomi)]]