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DOI: 10.14489/hb.supp.2019.01.pp.001-020
Горленко О. А., Борбаць Н. М.
КОВАРИАЦИОННЫЙ АНАЛИЗ
(с. 1-20)
Аннотация. При проведении различного рода экспериментов по исследованию взаимосвязи между некоторой зависимой переменной (откликом) и одной или несколькими категориальными независимыми переменными (факторами) встречаются ситуации, когда отклик также может зависеть от еще одной или нескольких переменных, которые не могут управляться экспериментатором, но могут наблюдаться вместе с зависимой переменной. В этом случае для повышения точности эксперимента применяется специальный вид статистического анализа – ковариационный анализ.
Ключевые слова: ковариационный анализ; однофакторный эксперимент; двухфакторный эксперимент; проверка гипотез.
Gorlenko O. A., Borbatc N. M.
ANALYSIS OF COVARIANCE
(pp. 1-20)
Abstract. In carrying out various experiments to investigate the relationship between a certain dependent variable (response) and one or more categorical independent variables (factors), there are situations where the response may also depend on one or more variables that can not be controlled by the experimenter, but can be observed together with a dependent variable. In this case, to increase the accuracy of the experiment, a special type of statistical analysis is used – covariance analysis.
Keywords: Covariance analysis; One-factor experiment; Two-factor experiment; Hypothesis testing.
О. А. Горленко, Н. М. Борбаць (Брянский государственный технический университет, Брянск, Россия) E-mail:
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O. A. Gorlenko, N. M. Borbatc (Bryansk State Technical University, Bryansk, Russia) E-mail:
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1. Winer B. J. Statistical Principles in Experimental Design. McGraw-Hill Book Company 1962, New-York, San-Francisco, Toronto, London. 680 р.
2. Фишер Р. А. Статистические методы для исследователей / пер. с англ. М.: Госстатиздат, 1958. 268 с.
3. Wildt A. R. and Ahtola O. T. (1978). Analysis of covariance (Sage University Paper Series on Quantitative Applications in the Social Sciences, series no. 07-012). Newbury Park, CA: Sage.
4. William G. Cochran. Analysis of Covariance: Its Nature and Uses. Biometrics. Special Issue on the Analysis of Covariance. Sep., 1957. V. 13, № 3. P. 261 – 281.
5. Fairfield Smith H. Interpretation of Adjusted Treatment Means and Regressions in Analysis of Covariance. Biometrics. Special Issue on the Analysis of Covariance. Sep., 1957. V. 13, № 3. P. 282 – 308.
6. Ronald D. Snee. A Note on the Use of Residuals for Examining the Assumptions of Covariance Analysis. Technometrics. May 1971. V. 13, № 2. P. 430 – 437.
7. James S. Degracie and Wayne A. Fuller. Estimation of the Slope and Analysis of Covariance When the Concomitant Variable is Measured with Error. Journal of the American Statistical Association. December 1972. V. 67, № 340. P. 930 – 937.
8. Atiquallah M. The Robustness of the Covariance Analysis of a One-way Classification. Biometrika. V. 51, № 3–4. 1964. P. 365 – 372.
9. Finney D. J. Stratification, Balance, and Covariance. Biometrics. Special Issue on the Analysis of Covariance. Sep., 1957. V. 13, № 3. P. 373 – 386.
10. Hazel L. N. The Covariance Analysis of Multiple Classification Tables with Unequal Subclass Numbers. Biometrics Bulletin. Apr., 1946. V. 2, № 2. P. 21 – 25.
11. Irma Coons. The Analysis of Covariance as a Missing Plot Technique. Biometrics. Special Issue on the Analysis of Covariance. Sep., 1957. V. 13, № 3. P. 387 – 405.
12. Wilkinson G. N. The Analysis of Covariance with Incomplete Data. Biometrics. Special Issue on the Analysis of Covariance. Sep., 1957. V. 13, № 3. P. 363 – 372.
13. Walter T. Federer. Variance and Covariance Analyses for Unbalanced Classifications. Biometrics. Special Issue on the Analysis of Covariance. Sep., 1957. V. 13, № 3. P. 333 – 362.
14. Zelen M. The Analysis of Covariance for Incomplete Block Designs. Biometrics. Special Issue on the Analysis of Covariance. Sep., 1957. V. 13, № 3. P. 309 – 332.
15. Jeanne T. Truitt and H. Fairfield Smith. Adjustment by Covariance and Consequent Tests of Significance in Split-Plot Experiments. Biometrics. Mar., 1956. V. 12, № 1. P. 23 – 39.
16. Acheson J. Duncan. Quality Control and Industrial Statistics. Revised Edition, 1959. Richard D. Irwin, INC Homewood, Illinois. 980 p.
17. Bradley E. Huitema. The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies. John Wiley & Sons, Inc., Hoboken, New Jersey, 2011. 666 p.
18. Ostle B. Statistics in Research: Basic Concepts and Techniques for Research Workers. The Iowa State University Press, 1963. 612 р.
19. Georg A. Milliken and Dallas E. Johnson. Analysis of Messy Data. Volume III: Analysis of Covariance. Chapman&Hall/CRC, 2002. 598 p.
20. Walter T. Federer. Experimental Design: Theory and Application. Second Printing. The Macmillan Company, New York, 1963. 608 p.
21. George W. Snedecor. Statistical Methods: Applied to Experiments in Agriculture and Biology. Indian Edition, Allied Pacific Private Limited, Bombay, 1967. 548 p.
22. Roger E. Kirk. Experimental Design: Procedures for the Behavioral Sciences. Third Edition. Brooks / Cole Publishing Company A Division of International Thomson Publishing Inc., 1995. 922 p.
23. Lyman Ott R. and Michael Longnecker. An Introduction to Statistical Methods and Data Analysis. Seventh Edition,Cengage Learning, Boston, 2015. 1192 p.
24. Hinkelmann K. and Kempthorne O. Design and Analysis of Experiments. V. 1: Introduction to Experimental Design. Second Edition, A John Wiley & Sons, Inc., 2008. 668 p.
25. Шеффе Г. Дисперсионный анализ / пер. с англ. Б. А. Севастьянова, В. П. Чистякова. М.: Наука, 1980. 512 с.
26. Кульбак С. Теория информации и статистика / пер. с англ. Д. И. Гордеева, А. В. Прохорова; под ред. А. Н. Колмогорова. М.: Наука, 1967. 408 с.
27. Кендалл М., Стьюарт А. Многомерный статистический анализ и временны́е ряды / пер. с англ. Э. Л. Пресмана, В. И. Ротаря; под ред. А. Н. Колмогорова, Ю. В. Прохорова. М.: Наука, 1976. 736 с.
28. Айвазян С. А., Енюков И. С., Мешалкин Л. Д. Прикладная статистика. Исследование зависимостей: справ. изд. / под ред. С. А. Айвазяна. М.: Финансы и статистика, 1985. 487 с.
29. Себер Дж. Линейный регрессионный анализ / пер. с англ. В. П. Носко; под ред. М. Б. Малютова. М.: Мир, 1980. 456 с.
30. Монтгомери Д. К. Планирование эксперимента и анализ данных / пер. с англ. Л.: Судостроение, 1980. 384 с.
31. Афифи С., Эйзен А. Статистический анализ. Подход с использованием ЭВМ / пер. с англ. М.: Мир, 1982. 488 с.
32. Болч Б., Хуань К. Дж. Многомерные статистические методы для экономики / пер. с англ. А. П. Плитмана; под ред. С. А. Айвазяна. М.: Статистика, 1979. 317 с.
33. Рыжов Э. В., Горленко О. А. Математические методы в технологических исследованиях / отв. ред. А. Г. Гавриш. Киев: Наук. думка, 1990. 184 с.
34. Джонсон Н., Лион Ф. Статистика и планирование эксперимента в технике и науке. Методы планирования эксперимента / пер. с англ. М.: Мир, 1981. 520 с.
1. Winer B. J. (1962). Statistical Principles in Experimental Design. McGraw-Hill Book Company, New-York, San-Francisco, Toronto, London.
2. Fisher R. A. (1958). Statistical methods for researchers. Moscow: Gosstatizdat. [in Russian language]
3. Wildt A. R. and Ahtola O. T. (1978). Analysis of covariance (Sage University Paper Series on Quantitative Applications in the Social Sciences, series no. 07-012). Newbury Park, CA: Sage.
4. William G. Cochran. (1957). Analysis of Covariance: Its Nature and Uses. Biometrics. Special Issue on the Analysis of Covariance, 13(3), pp. 261-281.
5. H. Fairfield Smith. (1957). Interpretation of Adjusted Treatment Means and Regressions in Analysis of Covariance. Biometrics. Special Issue on the Analysis of Covariance, 13(3), pp. 282-308.
6. Ronald D. Snee. (1971). A Note on the Use of Residuals for Examining the Assumptions of Covariance Analysis. Technometrics, 13(2), pp. 430-437.
7. James S. Degracie and Wayne A. Fuller. (1972). Estimation of the Slope and Analysis of Covariance When the Concomitant Variable is Measured with Error. Journal of the American Statistical Association, Vol. 67, 340, pp. 930-937.
8. Atiquallah M. (1964). The Robustness of the Covariance Analysis of a One-way Classification. Biometrika, 51(3–4), pp. 365-372.
9. Finney D. J. (1957). Stratification, Balance, and Covariance. Biometrics. Special Issue on the Analysis of Covariance, 13(3), pp. 373-386.
10. Hazel L. N. (1946). The Covariance Analysis of Multiple Classification Tables with Unequal Subclass Numbers. Biometrics Bulletin, Vol. 2, (2), pp. 21-25.
11. Irma Coons. (1957). The Analysis of Covariance as a Missing Plot Technique. Biometrics. Special Issue on the Analysis of Covariance, 13(3), pp. 387-405.
12. Wilkinson G. N. (1957). The Analysis of Covariance with Incomplete Data. Biometrics. Special Issue on the Analysis of Covariance, 13(3), pp. 363-372.
13. Walter T. Federer. (1957). Variance and Covariance Analyses for Unbalanced Classifications. Biometrics. Special Issue on the Analysis of Covariance, 13(3), pp. 333-362.
14. Zelen M. (1957). The Analysis of Covariance for Incomplete Block Designs. Biometrics. Special Issue on the Analysis of Covariance, 13(3), pp. 309-332.
15. Jeanne T. Truitt and H. Fairfield Smith. (1956). Adjustment by Covariance and Consequent Tests of Significance in Split-Plot Experiments. Biometrics, 12(1), pp. 23-39.
16. Acheson J. Duncan. (1959). Quality Control and Industrial Statistics. Revised Edition,. Richard D. Irwin, INC Homewood, Illinois.
17. Bradley E. Huitema. (2011). The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies. John Wiley & Sons, Inc., Hoboken, New Jersey.
18. Ostle B. (1963). Statistics in Research: Basic Concepts and Techniques for Research Workers. The Iowa State University Press.
19. Georg A. Milliken and Dallas E. Johnson. (2002). Analysis of Messy Data. Volume III: Analysis of Covariance. Chapman&Hall/CRC.
20. Walter T. Federer. (1963). Experimental Design: Theory and Application. Second Printing. The Macmillan Company, New York.
21. George W. Snedecor. (1967). Statistical Methods: Applied to Experiments in Agriculture and Biology. Indian Edition, Allied Pacific Private Limited, Bombay.
22. Roger E. Kirk. (1995). Experimental Design: Procedures for the Behavioral Sciences. Third Edition. Brooks. Cole Publishing Company A Division of International Thomson Publishing Inc.
23. R. Lyman Ott and Michael Longnecker. (2015). An Introduction to Statistical Methods and Data Analysis. Seventh Edition,Cengage Learning, Boston.
24. Klaus Hinkelmann and Oscar Kempthorne. (2008). Design and Analysis of Experiments. Vol. 1: Introduction to Experimental Design. Second Edition. A John Wiley & Sons, Inc.
25. Sheffe G. (1980). Variance analysis. Moscow: Nauka. [in Russian language]
26. Kul'bak S. (1967). Information Theory and Statistics. Moscow: Nauka. [in Russian language]
27. Kendall M., St'yuart A. (1976). Multivariate statistical analysis and time series. Moscow: Nauka. [in Russian language]
28. Ayvazyan S. A. (Ed.), Enyukov I. S., Meshalkin L. D. (1985). Application statistics. The study of addictions: reference book. Moscow: Finansy i statistika. [in Russian language]
29. Seber Dzh. (1980). Linear regression. Moscow: Mir. [in Russian language]
30. Montgomeri D. K. (1980). Experiment Planning and Data Analysis. Leningrad: Sudostroenie. [in Russian language]
31. Afifi S., Eyzen A. (1982). Statistical analysis. Computer Approach. Moscow: Mir. [in Russian language]
32. Bolch B., Huan' K. Dzh. (1979). Multidimensional statistical methods for economics. Moscow: Statistika. [in Russian language]
33. Gavrish A. G.(Ed.), Ryzhov E. V., Gorlenko O. A. (1990). Mathematical methods in technological research. Kiev: Naukova dumka. [in Russian language]
34. Dzhonson N., Lion F. (1981). Statistics and experiment planning in engineering and science. Experiment Planning Methods. Moscow: Mir. [in Russian language]
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