An introduction to multivariate statistical analyses. Part I. Theoretical background
Zygmunt Kaczmarek
Instytut Genetyki Roślin Polskiej Akademii Nauk w Poznaniu, Pracownia Biometrii (Poland)
Dariusz R. Mańkowski
d.mankowski@ihar.edu.plInstytut Hodowli i Aklimatyzacji Roślin, Państwowy Instytut Badawczy w Radzikowie, Pracownia Ekonomiki Nasiennictwa i Hodowli Roślin (Poland)
https://orcid.org/0000-0002-7499-8016
Abstract
Multivariate analyses are increasingly used in agricultural research. The widespread availability of statistical packages pursuing this type of analysis allows for their use. Then, the ability of appropriate application of the analysis and correct interpretation of its results becomes problematic. The paper discusses basic concepts of the multivariate analysis, the multivariate model of observations, the multivariate analysis of variance, the appropriate statistical tests and the multivariate methods for estimation of the objects’ similarity.
Keywords:
multivariate analysis, multivariate grouping, correlation matrix, covariance matrix, MANOVA, multivariate similarity measuresReferences
Anderberg M. R. 1973. Cluster Analysis for Applications. Academic Press, New York.
Google Scholar
Caliński T. 1970. Wielozmienna analiza wariancji i pokrewne metody wielowymiarowe. PAN, Warszawa.
Google Scholar
Caliński T., Czajka S., Kaczmarek Z. 1975. Analiza składowych głównych i jej zastosowania. Algorytmy biometryczne i statystyczne (ABS-36). AR Poznań.
Google Scholar
Caliński T., Dyczkowski A., Kaczmarek Z. 1976. Testowanie hipotez w wielozmiennej analizie wariancji i kowariancji. Algorytmy biometryczne i statystyczne (ABS-45). AR Poznań.
Google Scholar
Caliński T., Kaczmarek Z. 1973. Metody kompleksowej analizy doświadczenia wielocechowego. Trzecie Colloquium Metodologiczne z Agro-Biometrii, PAN i PTB Warszawa: 257 — 320.
Google Scholar
Ceranka B., Chudzik H., Kaczmarek Z., Krzyśko M. 1975. Wielozmienna analiza wyników doświadczeń w układach blokowych. Algorytmy biometryczne i statystyczne (ABS-35). AR Poznań.
Google Scholar
Everitt B. S., Dunn G. 1992. Applied Multivariate Data Analysis. Oxford University Press. New York.
Google Scholar
Kaczmarek Z. 1975. Wielozmienna analiza kowariancji i jej niektóre zastosowania. Matematyka Stosowana 5: 139 — 156.
Google Scholar
Kaczmarek Z., Czajka S., Adamska E. 2008. Propozycja metody grupowania obiektów jedno- i wielocechowych z zastosowaniem odległości Mahalanobisa i analizy skupień. Biul. IHAR 249: 9 — 18.
Google Scholar
Krzanowski W. J. 1988. Principles of multivariate analysis: a users’s perspective. Oxford University Press.
Google Scholar
Krzyśko M. 2000. Wielowymiarowa analiza statystyczna. Wydawnictwo Naukowe UAM, Poznań.
Google Scholar
Mądry W. 2007. Metody statystyczne do oceny różnorodności fenotypowej dla cech ilościowych w kolekcjach roślinnych zasobów genowych. Zesz. Probl. Post.-Nauk Rol. 517: 21 — 41.
Google Scholar
McKeon J. J. 1974. F approximations to the distribution of Hotelling's T20. Biometrika 61: 381 — 383.
Google Scholar
Morrison D. F. 1976. Multivariate Statistical Methods. McGraw-Hill. New York.
Google Scholar
Seber G. A. F. 1984. Multivariate Observations. Wiley. New York.
Google Scholar
Sieczko L., Mądry W., Zieliński A., Paderewski J., Urbaś-Szwed K. 2004. Zastosowanie analizy składowych głównych w badaniach nad wielocechową charakterystyką zmienności genetycznej w kolekcji zasobów genowych pszenicy twardej (Triticum durum L.). XXXIV Coll. Biometryczne: 223 — 239.
Google Scholar
Srivastava M. S. 2004. Multivariate theory for analyzing high-dimensional data. Technical Report, University of Toronto, Toronto, Canada.
Google Scholar
Ukalska J., Mądry W., Ukalski K., Masny A. 2007. Wielowymiarowa ocena różnorodności fenotypowej w kolekcji zasobów genowych truskawki. Cz. II. Grupowanie genotypów. Zeszyty Prob. Postępów Nauk Rolniczych 517: 759 — 766.
Google Scholar
Ukalska J., Ukalski K., Śmiałowski T., Mądry W. 2008. Badanie zmienności i współzależności cech użytkowych w kolekcji roboczej pszenicy ozimej (Triticum aestivum L.) za pomocą metod wielowymiarowych. Cz. II. Analiza składowych głównych na podstawie macierzy korelacji fenotypowych i genotypowych. Biul. IHAR 249: 45 — 57.
Google Scholar
Wu Y., Genton M. G., Stefanski L. A. 2006. A Multivariate two sample mean test for small sample size and missing data. Biometrics 62: 877 — 885.
Google Scholar
Authors
Zygmunt KaczmarekInstytut Genetyki Roślin Polskiej Akademii Nauk w Poznaniu, Pracownia Biometrii Poland
Authors
Dariusz R. Mańkowskid.mankowski@ihar.edu.pl
Instytut Hodowli i Aklimatyzacji Roślin, Państwowy Instytut Badawczy w Radzikowie, Pracownia Ekonomiki Nasiennictwa i Hodowli Roślin Poland
https://orcid.org/0000-0002-7499-8016
Statistics
Abstract views: 44PDF downloads: 17
License
Copyright (c) 2011 Zygmunt Kaczmarek, Dariusz R. Mańkowski
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Upon submitting the article, the Authors grant the Publisher a non-exclusive and free license to use the article for an indefinite period of time throughout the world in the following fields of use:
- Production and reproduction of copies of the article using a specific technique, including printing and digital technology.
- Placing on the market, lending or renting the original or copies of the article.
- Public performance, exhibition, display, reproduction, broadcasting and re-broadcasting, as well as making the article publicly available in such a way that everyone can access it at a place and time of their choice.
- Including the article in a collective work.
- Uploading an article in electronic form to electronic platforms or otherwise introducing an article in electronic form to the Internet or other network.
- Dissemination of the article in electronic form on the Internet or other network, in collective work as well as independently.
- Making the article available in an electronic version in such a way that everyone can access it at a place and time of their choice, in particular via the Internet.
Authors by sending a request for publication:
- They consent to the publication of the article in the journal,
- They agree to give the publication a DOI (Digital Object Identifier),
- They undertake to comply with the publishing house's code of ethics in accordance with the guidelines of the Committee on Publication Ethics (COPE), (http://ihar.edu.pl/biblioteka_i_wydawnictwa.php),
- They consent to the articles being made available in electronic form under the CC BY-SA 4.0 license, in open access,
- They agree to send article metadata to commercial and non-commercial journal indexing databases.
Most read articles by the same author(s)
- Tadeusz Śmiałowski, Anna Cieplicka, Dariusz R. Mańkowski, One and multi-variable characterization of spring barley (Hordeum vulgare L.) cultivars grown in Smolice Plant Breeding and tested in field breeding experiments in 2016 , Bulletin of Plant Breeding and Acclimatization Institute: No. 282 (2017): Regular issue
- Tadeusz Adamski, Maria Surma, Zygmunt Kaczmarek, Anetta Kuczyńska, Krzysztof Mikołajczak, Michał Kempa, Piotr Ogrodowicz, Elżbieta Adamska, Renata Trzeciak, Alina Anioła, Renata Holewińska , Studies on the effect of 1B/1R translocations on the efficiency of obtaining wheat DH lines and their technological value , Bulletin of Plant Breeding and Acclimatization Institute: No. 286 (2019): Special issue
- Elżbieta Małuszyńska, Dariusz R. Mańkowski, Seed sowing value of certified seed of winter wheat stored in storehouse , Bulletin of Plant Breeding and Acclimatization Institute: No. 297/298 (2022): Regular issue
- Tadeusz Oleksiak, Dagmara Bronisz, Dariusz R. Mańkowski, Marzena Iwańska, Analysis of yielding stability and wide adaptation degree of selected winter triticale (× Triticosecale Witt.) cultivars based on field production data , Bulletin of Plant Breeding and Acclimatization Institute: No. 282 (2017): Regular issue
- Dariusz R. Mańkowski, Michał Kwiatek, Introduction to Issue 300 of the Bulletin of Plant Breeding and Acclimatization Institute , Bulletin of Plant Breeding and Acclimatization Institute: No. 300 (2023): Regular issue
- Dariusz R. Mańkowski, Biological progress in breeding, seed technology and production of potato in Poland. Part I. Review of quantitative methods applied to estimate of breeding and cultivar progress , Bulletin of Plant Breeding and Acclimatization Institute: No. 251 (2009): Regular issue
- Maria Surma, Tadeusz Adamski, Zygmunt Kaczmarek, Paweł Krajewski, Quantitative genetics —review through the century , Bulletin of Plant Breeding and Acclimatization Institute: No. 250 (2008): Regular issue
- Zbigniew Laudański, Dariusz R. Mańkowski, Leszek Sieczko, Attempt to evaluate winter wheat cultivation technology on the basis of survey data from individual farms. Part I. Method of selection of cultivation technology , Bulletin of Plant Breeding and Acclimatization Institute: No. 244 (2007): Regular issue
- Dariusz R. Mańkowski, Tadeusz Oleksiak, Factors determining application of certified seed material in farms , Bulletin of Plant Breeding and Acclimatization Institute: No. 244 (2007): Regular issue
- Zbigniew Laudański, Dariusz R. Mańkowski, Małgorzata Flaszka, Exploratory factor analysis in studying the structure of multivariate observations , Bulletin of Plant Breeding and Acclimatization Institute: No. 263 (2012): Regular issue
Similar Articles
- Agnieszka Grądzielewska, Edyta Paczos-Grzęda, Daniela Gruszecka, Application of RAPD and ISSR methods to genetic similarity estimation of Greek Dasypyrum villosum (L.) P. Candargy populations , Bulletin of Plant Breeding and Acclimatization Institute: No. 253 (2009): Regular issue
- Andrzej Latusek, Henryk Bujak, Genotype-environment interaction for yield of winter rye cultivars cultivated with the two levels of agricultural technology in climate conditions of Lower Silesia , Bulletin of Plant Breeding and Acclimatization Institute: No. 265 (2012): Regular issue
- Tadeusz Łuczkiewicz, Jerzy Nawracała, Jan Bocianowski, Genetic analysis of quantitative traits of F1 generation of spring rape (Brassica napus L.) , Bulletin of Plant Breeding and Acclimatization Institute: No. 250 (2008): Regular issue
- Krzysztof Wójcik, Rafał Kuriata, Sylwia Lewandowska, Heritability and relationships between maize agricultural traits , Bulletin of Plant Breeding and Acclimatization Institute: No. 264 (2012): Regular issue
- Agnieszka Dobrzycka, Joanna Wolko, Jan Bocianowski, Kamila Nowosad, The characteristics of phenotypic variation in DH lines and hybrids of winter oilseed rape (Brassica napus L.) including yield related traits , Bulletin of Plant Breeding and Acclimatization Institute: No. 287 (2019): Special issue
- Jakub Paderewski, Wiesław Mądry, Use of AMMI model in the analysis of cultivar responses to environments , Bulletin of Plant Breeding and Acclimatization Institute: No. 263 (2012): Regular issue
- Edyta Paczos-Grzęda, Application of the RAPD and SSR methods to genetic similarity assessment of tetraploid species of the Avena L. genus , Bulletin of Plant Breeding and Acclimatization Institute: No. 252 (2009): Regular issue
- Krzysztof Ukalski, Joanna Ukalska, Tadeusz Śmiałowski, Wiesław Mądry, An examination of diversity and interrelationships among traits in a winter wheat (Triticum aestivum L.) germplasm collection by multivariate methods. Part I. Phenotypic and genotypic correlations , Bulletin of Plant Breeding and Acclimatization Institute: No. 249 (2008): Regular issue
- Sylwia Jędzura, Anna Szafrańska, Przemysław Matysik, Assessing the spring wheat quality for breeding program purpose , Bulletin of Plant Breeding and Acclimatization Institute: No. 297/298 (2022): Regular issue
- Marcin Praczyk, Jan Bocianowski, Grażyna Silska, Genetic analysis of fiber content in fibrous flax F1 hybrids , Bulletin of Plant Breeding and Acclimatization Institute: No. 260/261 (2011): Regular issue
<< < 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 > >>
You may also start an advanced similarity search for this article.