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: 46PDF downloads: 19
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 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
- 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
- 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
- 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
- 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
- Zygmunt Kaczmarek, Stanisław Czajka, Elżbieta Adamska, A proposed method for grouping uni- and multivariate treatments using Mahalanobis distance and cluster analysis , Bulletin of Plant Breeding and Acclimatization Institute: No. 249 (2008): Regular issue
- Monika Janaszek-Mańkowska, Dariusz R. Mańkowski, Janusz Kozdój, MLP artificial neural networks in predicting the yield if spring barley , Bulletin of Plant Breeding and Acclimatization Institute: No. 259 (2011): Regular issue
- Dariusz R. Mańkowski, Zbigniew Laudański, Monika Janaszek, The application of chosen similarity measures for binary data in multivariate analysis in molecular experiments , Bulletin of Plant Breeding and Acclimatization Institute: No. 262 (2011): Regular issue
- Karolina Krystkowiak, Tadeusz Adamski, Maria Surma, Zygmunt Kaczmarek, Anetta Kuczyńska, Agata Burtna, Renata Trzeciak, Variability of chosen technological traits of winter wheat hybrids in relation to composition of HMW glutenin subunits in parental forms , Bulletin of Plant Breeding and Acclimatization Institute: No. 260/261 (2011): Regular issue
Similar Articles
- Dariusz R. Mańkowski, Zbigniew Laudański, Monika Janaszek, The application of chosen similarity measures for binary data in multivariate analysis in molecular experiments , Bulletin of Plant Breeding and Acclimatization Institute: No. 262 (2011): Regular issue
- Joanna Ukalska, Krzysztof Ukalski, 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 II. Principal component analysis using the phenotypic and genotypic correlation matrix , Bulletin of Plant Breeding and Acclimatization Institute: No. 249 (2008): Regular issue
- Zygmunt Kaczmarek, Stanisław Czajka, Elżbieta Adamska, A proposed method for grouping uni- and multivariate treatments using Mahalanobis distance and cluster analysis , Bulletin of Plant Breeding and Acclimatization Institute: No. 249 (2008): Regular issue
- Dariusz Mańkowski, Janusz Wątroba, Covariates as an additional source of variability in the experiment , Bulletin of Plant Breeding and Acclimatization Institute: No. 300 (2023): Regular issue
- Wiesław Mądry, Marzena Iwańska, Usefulness of statistical methods and measures for evaluating cultivar stability and adaptation: an overview of research , Bulletin of Plant Breeding and Acclimatization Institute: No. 260/261 (2011): Regular issue
- Marcin Studnicki, Wiesław Mądry, Tadeusz Śmiałowski, Multivariate analysis of phenotypic diversity in Polish spring wheat collection , Bulletin of Plant Breeding and Acclimatization Institute: No. 252 (2009): Regular issue
- Wojciech Rybiński, Karolina Krystkowiak, Anetta Kuczyńska, Michał Rębarz, Variability of hull-less barley mutants (Hordeum vulgare L.) at the phenotypic and molecular levels , Bulletin of Plant Breeding and Acclimatization Institute: No. 245 (2007): Regular issue
- Tadeusz Śmiałowski, Maria Stachowicz, Multivariate analysis of the variability of traits determining technological quality of grains in strains and varieties of winter wheat assessed in pre-registration trials , Bulletin of Plant Breeding and Acclimatization Institute: No. 253 (2009): Regular issue
- Sylwia Okoń, Edyta Paczos-Grzęda, Piotr Kraska, Ewa Kwiecińska-Poppe, Edward Pałys, Assessment of genetic similarity of spelt (Triticum aestivum ssp. spelta L.) cultivars based on RAPD markers , Bulletin of Plant Breeding and Acclimatization Institute: No. 252 (2009): Regular issue
- Zygmunt Kaczmarek, Dariusz R. Mańkowski, An introduction to multivariate statistical analyses. Part II. The application , Bulletin of Plant Breeding and Acclimatization Institute: No. 259 (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.