Wilcoxon signed rank test

ウィルコクソン符号順位検定

WordNet

1. place signs, as along a road; "sign an intersection"; "This road has been signed"
2. (medicine) any objective evidence of the presence of a disorder or disease; "there were no signs of asphyxiation"
3. a perceptible indication of something not immediately apparent (as a visible clue that something has happened); "he showed signs of strain"; "they welcomed the signs of spring" (同)mark
4. a character indicating a relation between quantities; "dont forget the minus sign"
5. a fundamental linguistic unit linking a signifier to that which is signified; "The bond between the signifier and the signified is arbitrary"--de Saussure
6. a gesture that is part of a sign language
7. a public display of a message; "he posted signs in all the shop windows"
8. engage by written agreement; "They signed two new pitchers for the next season" (同)contract, sign on, sign_up
9. approve and express assent, responsibility, or obligation; "All parties ratified the peace treaty"; "Have you signed your contract yet?" (同)ratify
10. communicate silently and non-verbally by signals or signs; "He signed his disapproval with a dismissive hand gesture"; "The diner signaled the waiters to bring the menu" (同)signal, signalize, signalise
11. mark with ones signature; write ones name (on); "She signed the letter and sent it off"; "Please sign here" (同)subscribe
12. be engaged by a written agreement; "He signed to play the casino on Dec. 18"; "The soprano signed to sing the new opera"
13. communicate in sign language; "I dont know how to sign, so I could not communicate with my deaf cousin"
14. very offensive in smell or taste; "a rank cigar"
15. relative status; "his salary was determined by his rank and seniority"
16. a row or line of people (especially soldiers or police) standing abreast of one another; "the entrance was guarded by ranks of policemen"
17. take precedence or surpass others in rank (同)outrank
18. growing profusely; "rank jungle vegetation"
19. take or have a position relative to others; "This painting ranks among the best in the Western World"
20. very fertile; producing profuse growth; "rank earth"
21. undergo a test; "She doesnt test well"
22. any standardized procedure for measuring sensitivity or memory or intelligence or aptitude or personality etc; "the test was standardized on a large sample of students" (同)mental test, mental testing, psychometric test
23. the act of undergoing testing; "he survived the great test of battle"; "candidates must compete in a trial of skill" (同)trial
24. the act of testing something; "in the experimental trials the amount of carbon was measured separately"; "he called each flip of the coin a new trial" (同)trial, run
25. a hard outer covering as of some amoebas and sea urchins
26. put to the test, as for its quality, or give experimental use to; "This approach has been tried with good results"; "Test this recipe" (同)prove, try, try out, examine, essay
27. achieve a certain score or rating on a test; "She tested high on the LSAT and was admitted to all the good law schools"
28. determine the presence or properties of (a substance)
29. show a certain characteristic when tested; "He tested positive for HIV"
30. an examination of the characteristics of something; "there are laboratories for commercial testing"; "it involved testing thousands of children for smallpox"
31. the act of subjecting to experimental test in order to determine how well something works; "they agreed to end the testing of atomic weapons"
32. having a higher rank; "superior officer" (同)superior, higher-ranking
33. position on a scale in relation to others in a sport

PrepTutorEJDIC

1. (ある事実・状態・感情などの)『表れ』,印,気配,徴侯(indication);(…の)こん跡,計跡《+『of』+『名』》・『身ぶり』,手まね,合図 / 『標識』,看板 / (数学・音楽などの)記号 / (…の)『象徴』,シンボル(symbol)《+『of』+『名』》・《文》(…の)『前兆』,きざし《+『of』+『名』》・宮(きゅう)(黄道12区分の一つ) ・〈手紙・書類・作品など〉‘に'『署名する』・(…に)〈名前など〉‘を'書く《+『名』+『on』(『to』)+『名』》 / …‘を'雇う契約に署名する・…‘を'合図する,知らせる;…に合図する・署名する・契約書に署名して雇われる
2. 〈C〉〈U〉『階級』,等級;)相対的な)『順位』,地位: / 〈U〉高い地位(身分) / 〈C〉〈U〉(人・物の)『列』,並び;(兵隊)の横列 / 《the ranks》(また『rank and file』)(将校たちに対して)兵卒,下士官 / …‘を'『並べる』 / …‘を'『位置づける』,評価する / 《米》…‘より'上位にある / 『位置する』・「pull one's rank on 誰々」で「(誰々に)地位を悪用する; (意見が衝突したような場合に)階級をかさに着て(誰々に)命令を押しつける」
3. (植物が)おい茂った,はびこった / (土地が)植物をおい茂らせた,肥えすぎた;(土地が)(植物を)おい茂らせた《+『with』+『名』》 / 悪臭を放つ,いやな味のする / 全くの,ひどい
4. (人の能力などの)『試験』,考査,テスト / (物事の)『試験』,検済,試錬,実験《+of+名》 / 化学分析;試薬 / =test match / …‘を'『試験する』,検査する / …‘を'化学分析する / (…の)試験を受ける,試験をする《+for+名》
5. 上位の,一流の,卓越した

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/01/11 19:11:48」(JST)

wiki en

[Wiki en表示]

The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed.

The test is named for Frank Wilcoxon (1892–1965) who, in a single paper, proposed both it and the rank-sum test for two independent samples (Wilcoxon, 1945). The test was popularized by Siegel (1956) in his influential text book on non-parametric statistics. Siegel used the symbol T for the value defined below as . In consequence, the test is sometimes referred to as the Wilcoxon T test, and the test statistic is reported as a value of T. Other names may include the "t-test for matched pairs" or the "t-test for dependent samples".

Assumptions

1. Data are paired and come from the same population.
2. Each pair is chosen randomly and independent.
3. The data are measured on an interval scale (ordinal is not sufficient because we take differences), but need not be normal.

Test procedure

Let be the sample size, the number of pairs. Thus, there are a total of 2N data points. For , let and denote the measurements.

.

1. For , calculate and , where is the sign function.
2. Exclude pairs with . Let be the reduced sample size.
3. Order the remaining pairs from smallest absolute difference to largest absolute difference, .
4. Rank the pairs, starting with the smallest as 1. Ties receive a rank equal to the average of the ranks they span. Let denote the rank.
5. Calculate the test statistic

   , the absolute value of the sum of the signed ranks.

6. As increases, the sampling distribution of converges to a normal distribution. Thus,

   For , a z-score can be calculated as .

   If then reject

   
   

   For , is compared to a critical value from a reference table.

   
   

   If then reject

   
   

   Alternatively, a p-value can be calculated from enumeration of all possible combinations of given .

Example

1 125 110 1 15 2 115 122  –1 7 3 130 125 1 5 4 140 120 1 20 5 140 140   0 6 115 124  –1 9 7 140 123 1 17 8 125 137  –1 12 9 140 135 1 5 10 135 145  –1 10

order by absolute difference

5 140 140   0     3 130 125 1 5 1.5 1.5 9 140 135 1 5 1.5 1.5 2 115 122  –1 7 3  –3 6 115 124  –1 9 4  –4 10 135 145  –1 10 5  –5 8 125 137  –1 12 6  –6 1 125 110 1 15 7 7 7 140 123 1 17 8 8 4 140 120 1 20 9 9

is the sign function, is the absolute value, and is the rank. Notice that pairs 3 and 9 are tied in absolute value. They would be ranked 1 and 2, so each gets the average of those ranks, 1.5.

See also

• Mann-Whitney-Wilcoxon test (the variant for two independent samples)
• Sign test (Like Wilcoxon test, but without the assumption of symmetric distribution of the differences around the median, and without using the magnitude of the difference)

References

External links

• Description of how to calculate p for the Wilcoxon signed-ranks test
• Example of using the Wilcoxon signed-rank test
• An online version of the test
• A table of critical values for the Wilcoxon signed-rank test
• Discussion and table of critical values for the original Wilcoxon Rank-Sum Test, which uses a slightly different test statistic (pdf)

Implementations

• ALGLIB includes implementation of the Wilcoxon signed-rank test in C++, C#, Delphi, Visual Basic, etc.
• The free statistical software R includes an implementation of the test as wilcox.test(x,y, paired=TRUE), where x and y are vectors of equal length.
• GNU Octave implements various one-tailed and two-tailed versions of the test in the wilcoxon_test function.
• SciPy includes an implementation of the Wilcoxon signed-rank test in Python

UpToDate Contents

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English Journal

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Japanese Journal

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• Magnetic Resonance in Medical Sciences, 2014
• … These coefficients were compared between Bayesian and oSVD using Wilcoxon's signed rank test. …
• NAID 130003392992

Related Links

• ウィルコクソンの符号順位検定 - Wikipedia

ウィルコクソンの符号順位検定（ふごうじゅんいけんてい、Wilcoxon signed-rank test） は一対の標本によるノンパラメトリック検定法である。t検定に対応し、t検定で必要とされ る仮定が満たされない場合に用いる。ウィルコクソン（Frank Wilcoxon、1892-1965） ...

• 私のための統計処理ー検定ー2群の比較

→parametric---, Student t-test：スチューデントのt検定（2標本t検定）. →non- parametric---, Mann-Whitney's U test：マン・ホイットニ検定 ＝Wilcoxon rank sum test（注：Wilcoxon signed rank testではない。） ...

Related Pictures

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★リンクテーブル★

リンク元	「ウィルコクソンの符号付き順位検定」「ウィルコクソン符号順位検定」
関連記事	「rank」「sign」「testing」「RANK」「test」

「ウィルコクソンの符号付き順位検定」

　　[★]

英

Wilcoxon signed rank test

「ウィルコクソン符号順位検定」

　　[★]

英

Wilcoxon signed rank test

「rank」

　　[★]

• n.

• 地位、順位。下級、投球
• 後位、養殖
• 列、並び。整列

• vt.

• 並べる、整列させる。(～と)並べる、同列にする
• ～に等級(順位)をつける、ランク付けをする。評価する。分類する。
• ～より階級が上だ、～の上に立つ

• vi.

• 位する、ランク付けされる。評価される。列する、並ぶ
• 上位を占める
• 整列する

関

lie、locate、location、loci、locus、map、position、ranking、sit、situated、situation、stand、topo

　 　 　 　 　 　 　 　 　

「sign」

　　[★]

• n.

• 徴候、兆候、サイン、(数学)符号

関

indication、manifestation、signature、stigma、stigmata、symptom、symptomatic

　 　 　 　 　 　 　 　 　 　 　 　 　 　

「testing」

　　[★]

• n.

• 試験

関

assessment、data quality、exam、examination、examine、experimental design、matched group、measurement、research design、scoring method、test、trial

　 　

「RANK」

　　[★]

• NFκB活性化受容体

関

receptor activator of nuclear factor-kappa B、receptor activator of nuclear factor-kappaB

同

receptor activator for nuclear factor kB

「test」

　　[★] テスト