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Exact nonparametrics in APL

Authors:

Bernd Streitberg,

Joachim RöhmelAuthors Info & Claims

ACM SIGAPL APL Quote Quad, Volume 14, Issue 4

Pages 313 - 325

https://doi.org/10.1145/384283.801115

Published: 01 June 1984 Publication History

Abstract

The authors present a new algorithm for the exact distribution of many nonparametric tests. The algorithm is based on a recursion formula that relates the distribution of where K₁,...,K_n are iid Bernoulli [1/2] and a₁,...,a_n are fixed p-vectors, to the distribution of T_n-1. The core idea is to realize this recursion by shifts of the p - dimensional distribution of T_n-1 in the computer main storage, which can be implemented efficiently in APL. We believe, that the method has achieved a breakthrough in the practical application of Fisher-Pitman permutation tests, but it can also be used routinely in the computation of many other tests by applying an initial transformation to the original data. A noteworthy example is the Wilcoxon test with arbitrary ties in the data, whose exact distribution can easily be computed for Nample 100.

In order to allow the direct use of these results, a complete list of the necessary APL programmes is included in the text.

References

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https://doi.org/10.1016/j.joep.2012.07.009
Hirji K(2010)ReferencesExact Analysis of Discrete Data10.1201/9781420036190.bmatt(485-513)Online publication date: 28-Jan-2010
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Index Terms

Exact nonparametrics in APL
1. Mathematics of computing
  1. Probability and statistics
    1. Nonparametric statistics
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types

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Information & Contributors

Information

Published In

cover image ACM SIGAPL APL Quote Quad

ACM SIGAPL APL Quote Quad Volume 14, Issue 4

June 1984

362 pages

ISSN:0163-6006

DOI:10.1145/384283

Issue’s Table of Contents

APL '84: Proceedings of the international conference on APL
June 1984
391 pages
ISBN:0897911377
DOI:10.1145/800058
Chairman:
Sten Kallin

Copyright © 1984 Authors.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1984

Published in SIGAPL Volume 14, Issue 4

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Cited By

Klappe EHeijmans JGroen Kter Schure JCornet Rde Keizer N(2023)Correctly structured problem lists lead to better and faster clinical decision-making in electronic health records compared to non-curated problem lists: a single-blinded crossover randomized controlled trialInternational Journal of Medical Informatics10.1016/j.ijmedinf.2023.105264(105264)Online publication date: Oct-2023
https://doi.org/10.1016/j.ijmedinf.2023.105264
Fischer SGüth W(2012)Effects of exclusion on acceptance in ultimatum gamesJournal of Economic Psychology10.1016/j.joep.2012.07.00933:6(1100-1114)Online publication date: Dec-2012
https://doi.org/10.1016/j.joep.2012.07.009
Hirji K(2010)ReferencesExact Analysis of Discrete Data10.1201/9781420036190.bmatt(485-513)Online publication date: 28-Jan-2010
https://doi.org/10.1201/9781420036190.bmatt
Röhmel J(2007)Precision Intervals for Estimates of the Difference in Success Rates for Binary Random Variables Based on the Permutation PrincipleBiometrical Journal10.1002/bimj.471038081038:8(977-993)Online publication date: 18-Jan-2007
https://doi.org/10.1002/bimj.4710380810
Hothorn TWinell HHornik Kvan de Wiel MZeileis A(2005)coin: Conditional Inference Procedures in a Permutation Test FrameworkCRAN: Contributed Packages10.32614/CRAN.package.coinOnline publication date: 25-Feb-2005
https://doi.org/10.32614/CRAN.package.coin
Kieser MRöhmel JFriede T(2004)Power and sample size determination when assessing the clinical relevance of trial results by ‘responder analyses’Statistics in Medicine10.1002/sim.191023:21(3287-3305)Online publication date: 18-Oct-2004
https://doi.org/10.1002/sim.1910
Hirji K(1997)A comparison of algorithms for exact goodness-of-fit tests for multinomial dataCommunications in Statistics - Simulation and Computation10.1080/0361091970881343526:3(1197-1227)Online publication date: Jan-1997
https://doi.org/10.1080/03610919708813435
Hirji K(1997)A review and a synthesis of the fast Fourier transform algorithms for exact analysis of discrete dataComputational Statistics & Data Analysis10.1016/S0167-9473(97)00008-X25:3(321-336)Online publication date: 21-Aug-1997
https://dl.acm.org/doi/10.1016/S0167-9473%2897%2900008-X
Baglivo JPagano MSpino C(1996)Permutation Distributions via Generating Functions with Applications to Sensitivity Analysis of Discrete DataJournal of the American Statistical Association10.1080/01621459.1996.1047697491:435(1037-1046)Online publication date: Sep-1996
https://doi.org/10.1080/01621459.1996.10476974
Herrmann WKubicki SBoden SEich FAttali PCoquelin J(1993)Pilot Controlled Double-Blind Study of the Hypnotic Effects of Zolpidem in Patients with Chronic ‘Learned’ Insomnia: Psychometric and Polysomnographic EvaluationJournal of International Medical Research10.1177/03000605930210060221:6(306-322)Online publication date: 1-Nov-1993
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