Covariates as an additional source of variability in the experiment

Dariusz Mańkowski

d.mankowski@ihar.edu.pl
Plant Breeding and Acclimatization Institute - National Research Institute (Poland)
https://orcid.org/0000-0002-7499-8016

Janusz Wątroba


StatSoft Polska Sp. z o. o. (Poland)

Abstract

Covariates characterize and complement the variables analyzed in the experiment. They can explain various reactions of observed experimental units to the studied phenomenon or process. The basic statistical tools used to analyze experimental data considering covariates are regression analysis and analysis of covariance. While regression function analysis is a method often used in the analysis of experimental data, this is not the case with analysis of covariance. There are relatively few works presenting the practical use of this method. The aim of this paper is to present the analysis of covariance and its practical use. The paper describes the method of analysis of covariance on the example of a single classification and its use is shown in two agronomical examples.


Keywords:

data analysis, ANCOVA, covariates, mathematical statistics

Bickel, P.J., Hammel, E.A., O’Connell, J.W., 1975. Sex Bias in Graduate Admissions: Data from Berkeley. Science 187, 398–404. DOI: https://doi.org/10.1126/science.187.4175.398
Google Scholar

Cochran, W.G., Cox, G.M., 1992. Experimental design. John Wiley & Sons Inc., Hoboken, USA.
Google Scholar

Elandt, R., 1964. Statystyka matematyczna w zastosowaniu do doświadczalnictwa rolniczego. PWN, Warszawa.
Google Scholar

Kievit, R., Frankenhuis, W., Waldorp, L., Borsboom, D., 2013. Simpson’s paradox in psychological science: a practical guide. Front. Psychol. 4.
Google Scholar

Linnik, J.W., 1962. Metoda najmniejszych kwadratów i teoria opracowywania obserwacji. PWN, Warszawa.
Google Scholar

McConnell, T.E., Shi, S.Q., Chen, H., Wang, G., 2014. Differences Observed in Data Analysis Techniques: An Example Using Natural Fibers’ Diameters and Absorption Times. Appl. Eng. Agric. 55–58. DOI: https://doi.org/10.13031/aea.30.10242
Google Scholar

Montgomery, D.C., 2005. Design and analysis of experiments. 6th edition. John Wiley & Sons Inc., Hoboken, NJ, USA.
Google Scholar

Oktaba, W., 1971. Metody statystyki matematycznej w doświadczalnictwie. PWN.
Google Scholar

Paterson, D.D., 1939. Statistical Technique in Agricultural Research: A Simple Exposition of Practice and Procedure in Biometry, McGraw-Hill publications in the agricultural sciences. McGraw-Hill.
Google Scholar

Pearson, K., Lee, A., Bramley-Moore, L., 1899. VI. Mathematical contributions to the theory of evolution. —VI. Genetic (reproductive) selection: Inheritance of fertility in man, and of fecundity in thoroughbred racehorses. Philos. Trans. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character 192, 257–330. DOI: https://doi.org/10.1098/rsta.1899.0006
Google Scholar

Simpson, E.H., 1951. The interpretation of Interaction in Contingency Tables. J. R. Stat. Soc. Ser. B Methodol. 13, 238–241.
Google Scholar

Stanisz, A., 2007. Przystępny kurs statystyki z zastosowaniem STATISTICA na przykładach z medycyny. Tom 2. Modele liniowe i nieliniowe., wyd. 3. StatSoft Polska Sp. z o.o., Kraków.
Google Scholar

Szklarska, J., Walewski, R., Pielat, H., Radzikowska, A., 1978. Wybrane metody statystyki matematycznej w doświadczalnictwie rolniczym i warzywniczym. Część 1., II. ed PWRiL, Poznań.
Google Scholar

TIBCO Software Inc., 2017. Statistica (data analysis software system). Version 13. http://statistica.io.
Google Scholar

Timm, N.H., 2002. Applied multivariate analysis. Springer-Verlag Inc., New York, USA.
Google Scholar

Wijesuriya, B.W., Thattil, R.O., 1996. Use of Covariates in Improving Precision of Field Experiments in Rubber. Trop. Agric. Res. 20–29.
Google Scholar

Wójcik, A.R., Laudański, Z., 1989. Planowanie i wnioskowanie statystyczne w doświadczalnictwie. PWN, Warszawa.
Google Scholar

Yang, R.-C., Juskiw, P., 2011. Analysis of covariance in agronomy and crop research. Can. J. Plant Sci. 91, 621–641. DOI: https://doi.org/10.4141/cjps2010-032
Google Scholar

Yule, U.G., 1903. Notes on the Theory of Association of Attributes in Statistics. DOI: https://doi.org/10.1093/biomet/2.2.121
Google Scholar


Published
2023-12-29

Cited by

Mańkowski, D. and Wątroba, J. (2023) “Covariates as an additional source of variability in the experiment”, Bulletin of Plant Breeding and Acclimatization Institute, (300), pp. 23–32. doi: 10.37317/biul-2023-0009.

Authors

Dariusz Mańkowski 
d.mankowski@ihar.edu.pl
Plant Breeding and Acclimatization Institute - National Research Institute Poland
https://orcid.org/0000-0002-7499-8016

Authors

Janusz Wątroba 

StatSoft Polska Sp. z o. o. Poland

Statistics

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