WordNet

pregnancy test that involves injecting some of the womans urine into an unmated female rabbit and later examining the ovaries of the rabbit; presence of corpora lutea indicates that the woman is pregnant (同)rabbit test
undergo a test; "She doesnt test well"
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
the act of undergoing testing; "he survived the great test of battle"; "candidates must compete in a trial of skill" (同)trial
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
a hard outer covering as of some amoebas and sea urchins
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
achieve a certain score or rating on a test; "She tested high on the LSAT and was admitted to all the good law schools"
determine the presence or properties of (a substance)
show a certain characteristic when tested; "He tested positive for HIV"
an examination of the characteristics of something; "there are laboratories for commercial testing"; "it involved testing thousands of children for smallpox"
the act of subjecting to experimental test in order to determine how well something works; "they agreed to end the testing of atomic weapons"
tested and proved useful or correct; "a tested method" (同)tried, well-tried
tested and proved to be reliable (同)time-tested, tried, tried and true
United States economist noted as a proponent of monetarism and for his opposition to government intervention in the economy (born in 1912) (同)Milton Friedman

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(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》
testis の複数形

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/05/28 17:17:11」(JST)

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The Friedman test is a non-parametric statistical test developed by the U.S. economist Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or block) together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test.

Classic examples of use are:

n wine judges each rate k different wines. Are any wines ranked consistently higher or lower than the others?
n wines are each rated by k different judges. Are the judges' ratings consistent with each other?
n welders each use k welding torches, and the ensuing welds were rated on quality. Do any of the torches produce consistently better or worse welds?

The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal-Wallis one-way analysis of variance by ranks.

Friedman test is widely supported by many statistical software packages.

Method

Given data , that is, a matrix with rows (the blocks), columns (the treatments) and a single observation at the intersection of each block and treatment, calculate the ranks within each block. If there are tied values, assign to each tied value the average of the ranks that would have been assigned without ties. Replace the data with a new matrix where the entry is the rank of within block .
Find the values:
- ,
The test statistic is given by . Note that the value of Q as computed above does not need to be adjusted for tied values in the data.
Finally, when n or k is large (i.e. n > 15 or k > 4), the probability distribution of Q can be approximated by that of a chi-squared distribution. In this case the p-value is given by . If n or k is small, the approximation to chi-square becomes poor and the p-value should be obtained from tables of Q specially prepared for the Friedman test. If the p-value is significant, appropriate post-hoc multiple comparisons tests would be performed.

Related tests

When using this kind of design for a binary response, one instead uses the Cochran's Q test.
Kendall's W is a normalization of the Friedman statistic between 0 and 1.
The Wilcoxon signed-rank test is a nonparametric test of nonindependent data from only two groups.

Post hoc analysis

Post-hoc tests were proposed by Schaich and Hamerle (1984)^[1] as well as Conover (1971, 1980)^[2] in order to decide which groups are significantly different from each other, based upon the mean rank differences of the groups. These procedures are detailed in Bortz, Lienert and Boehnke (2000, pp. 275).^[3]

Not all statistical packages support Post-hoc analysis for Friedman's test, but user-contributed code exists that provides these facilities (for example in SPSS [1], and in R [2])

References

^ Schaich, E. & Hamerle, A. (1984). Verteilungsfreie statistische Prüfverfahren. Berlin: Springer. ISBN 3-540-13776-9.
^ Conover, W. J. (1971, 1980). Practical nonparametric statistics. New York: Wiley. ISBN 0-471-16851-3.
^ Bortz, J., Lienert, G. & Boehnke, K. (2000). Verteilungsfreie Methoden in der Biostatistik. Berlin: Springer. ISBN 3-540-67590-6.

Primary sources

Friedman, Milton (December 1937). "The use of ranks to avoid the assumption of normality implicit in the analysis of variance". Journal of the American Statistical Association (American Statistical Association) 32 (200): 675–701. doi:10.2307/2279372. JSTOR 2279372.
Friedman, Milton (March 1939). "A correction: The use of ranks to avoid the assumption of normality implicit in the analysis of variance". Journal of the American Statistical Association (American Statistical Association) 34 (205): 109. doi:10.2307/2279169. JSTOR 2279169.
Friedman, Milton (March 1940). "A comparison of alternative tests of significance for the problem of m rankings". The Annals of Mathematical Statistics 11 (1): 86–92. doi:10.1214/aoms/1177731944. JSTOR 2235971.

Secondary sources

Kendall, M. G. Rank Correlation Methods. (1970, 4th ed.) London: Charles Griffin.
Hollander, M., and Wolfe, D. A. Nonparametric Statistics. (1973). New York: J. Wiley.
Siegel, Sidney, and Castellan, N. John Jr. Nonparametric Statistics for the Behavioral Sciences. (1988, 2nd ed.) New York: McGraw-Hill.

External links

Post-hoc comparisons for Friedman test in SPSS
Post hoc analysis for Friedman’s Test in R

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English Journal

Cold-water immersion alters muscle recruitment and balance of basketball players during vertical jump landing.

Macedo Cde S1, Vicente RC1, Cesário MD1, Guirro RR1.
Journal of sports sciences.J Sports Sci.2016 Feb;34(4):348-57. doi: 10.1080/02640414.2015.1054861. Epub 2015 Jun 10.
The purpose of this study was to evaluate the effects of cold-water immersion on the electromyographic (EMG) response of the lower limb and balance during unipodal jump landing. The evaluation comprised 40 individuals (20 basketball players and 20 non-athletes). The EMG response in the lateral gastr
PMID 26058795

Women With Gestational Diabetes Mellitus Randomized to a Higher-Complex Carbohydrate/Low-Fat Diet Manifest Lower Adipose Tissue Insulin Resistance, Inflammation, Glucose, and Free Fatty Acids: A Pilot Study.

Hernandez TL1, Van Pelt RE2, Anderson MA2, Reece MS3, Reynolds RM4, de la Houssaye BA4, Heerwagen M4, Donahoo WT5, Daniels LJ6, Chartier-Logan C3, Janssen RC4, Friedman JE4, Barbour LA7.
Diabetes care.Diabetes Care.2016 Jan;39(1):39-42. doi: 10.2337/dc15-0515. Epub 2015 Jul 29.
OBJECTIVE: Diet therapy in gestational diabetes mellitus (GDM) has focused on carbohydrate restriction but is poorly substantiated. In this pilot randomized clinical trial, we challenged the conventional low-carbohydrate/higher-fat (LC/CONV) diet, hypothesizing that a higher-complex carbohydrate/low
PMID 26223240

Assessment of Apical Extrusion during Root Canal Irrigation with the Novel GentleWave System in a Simulated Apical Environment.

Charara K1, Friedman S2, Sherman A3, Kishen A2, Malkhassian G2, Khakpour M3, Basrani B2.
Journal of endodontics.J Endod.2016 Jan;42(1):135-9. doi: 10.1016/j.joen.2015.04.009. Epub 2015 Nov 4.
INTRODUCTION: This study assessed apical extrusion during treatment with GentleWave (GW; Sonendo Inc, Laguna Hills, CA), a conventional open-ended 30-G needle (CN), or Endovac (EV; SybronEndo, Orange, CA) in root canals enlarged to different dimensions with and without apical constriction.METHODS:
PMID 26547720

Japanese Journal

Season-Induced Changes in Bovine Sperm Motility Following a Freeze-Thaw Procedure

ORGAL Shlomo,ZERON Yoel,ELIOR Nili [他],BIRAN David,FRIEDMAN Eran,DRUKER Shaked,ROTH Zvi
The Journal of reproduction and development 58(2), 212-218, 2012-04-01
… Acrosome integrity was assessed by a triple-fluorescence test using Hoechst 33342, fluorescein isothiocyanate-conjugated Pisum sativum agglutinin (FITC-PSA) and propidium iodide. …
NAID 10030753852

FDG-PET/CT-based Gross Tumor Volume Contouring for Radiation Therapy Planning: An Experimental Phantom Study

TOYA Ryo,MURAKAMI Ryuji,TASHIRO Kuniyuki [他],YOSHIDA Morikatsu,SAKAMOTO Fumi,KAWANAKA Koichi,SHIRAISHI Shinya,NAKAGUCHI Yuji,TSUJITA Naoko,OYA Natsuo,TOMIGUCHI Seiji,YAMASHITA Yasuyuki
Journal of Radiation Research 53(2), 338-341, 2012
… The threshold ratio and the volume ratio in 6 spheres with 3 SBRs were compared using the Friedman test. …
NAID 130001876819

社会的スキルと表情表出時の顔面形状の関係(顔とコミュニケーション)

上出寛子,小森政嗣,川村智 [他],長岡千賀
電子情報通信学会技術研究報告. HCS, ヒューマンコミュニケーション基礎 111(214), 7-12, 2011-09-16
… び幾何学的形態測定手法を用いて検討した.日本人の学生(n=62)が基本感情のうち代表的な真顔,幸福,怒りの表情を表出し,さらにコミュニケーションの表出性を測定する感情的コミュニケーション・テスト(ACT;Friedman et al.,1980)に回答した.36点の標識点座標を顔形状データから取得し,幾何学的形態測定学的手法により標識点を標準化し,さらにこれらの標識点座標値に対し主成分分析を行った.その結果,ACT得点は,いくつかの …
NAID 110008900616