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biometrics, in biology
a branch of biology concerned with planning and interpreting the results of quantitative experiments and observations by the methods of mathematical statistics. In conducting biological experiments and observations an investigator always has to deal with quantitative variations in the frequency of occurrence or degree of manifestation of different characteristics and properties. Hence, without special statistical analysis it is usually impossible to determine what the possible limits of random variations may be and whether the observed differences between the experimental versions are accidental or significant. Mathematical statistical methods as used in biology are sometimes developed without reference to biological research. More often, however, they are related to the problems that arise in biology, agriculture, and medicine.
Biometry as an independent discipline developed at the end of the 19th century as a result of the work of the Englishman F. Galton, who made a major contribution to the creation of correlation and regression analysis, and K. Pearson, the founder of the most important school of biometry. Pearson analyzed in detail the main types of distributions found in biology. He developed the theory of correlation and proposed one of the best-known statistical methods, the “chisquare” criterion. The methodology of modern biometry was developed by R. A. Fisher (England), who founded his own school of biometry. Fisher was the first to show that planning experiments and observations and interpreting the results are two inseparable aspects of statistical analysis. He laid the foundations for the theory of experiment planning and proposed several efficient statistical methods (chiefly, dispersion [variance] analysis) which naturally emerge from the peculiarities of biological experiments. He also elaborated the theory of small samples first advanced by the English scientist Student (W. Gosset). The Russian scientists V. I. Romanovskii, A. A. Sapegin, Iu. A. Filipchenko, S. S. Chetverikov, and others played an important part in spreading biometric ideas and methods.
The use of mathematical statistical methods in biology essentially involves choosing some statistical model, checking to see that it conforms to the experimental data, and analyzing the statistical and biological results that it produces. The choice of a particular model is largely determined by the biological nature of the experiment. Any model contains a number of assumptions that must be tested in the experiment: for instance, the randomness of the choice of objects from a general set and, very commonly, the specific type of distribution of the random quantity to be investigated. The design of experiments has become an independent branch of biometry, which has several methods of effectively staging experiments at its disposal (such as different systems of dispersion analysis, sequential analysis, and design of screening experiments). These methods are of value in reducing the scope of an experiment to obtain the same amount of information. Three main statistical problems arise in interpreting the results of experiments and observations: (1) evaluation of the parameters of distribution—mean, dispersion, and so on (for example, establishing the limits of random variations in the number of patients who show improvement when treated with some drug under trial); (2) comparison of the parameters of different samples (for example, determining whether the difference between average yields of wheat varieties under study are accidental or significant); (3) detection of statistical relations—correlation, regression (for example, study of the correlation between the size or mass of different animal organs or study of the relationship between the frequency of cell injury and dose of ionizing radiation). The methods of multidimensional statistics are particularly useful in solving experimental problems because they make it possible to evaluate simultaneously the effect of several different factors and the interaction between them. These methods are being increasingly used to solve problems in taxonomy. Nonparametric methods without assumptions concerning the nature of the distribution of random quantities have become popular, but they are not as effective as parametric methods. Because of practical needs intensive efforts are being made to develop methods for studying heredity, sampling methods, and methods for studying dynamic processes (temporal series).
Articles on biometry are published in the journals Biometrika (London, 1901—), Biometrics (Atlanta, 1945—), and Biometrische Zeitschrift (Berlin, 1959—) and in various biological, agricultural, and medical journals.
REFERENCESBailey, N. Statisticheskie metody ν biologii. Moscow, 1963. (Translated from English.)
Rokitskii, P. F. Biologicheskaia statistika, 2nd ed. Minsk, 1967.
Snedecor, G. W. Statisticheskie metody ν primenenii k issledovaniiam ν sel’skom khoziaistve i biologii. Moscow, 1961. (Translated from English.)
Urbakh, V. Iu. Biometricheskie metody, 2nd ed. Moscow, 1964.
Finney, D. J. Primenenie statistiki ν opytnom dele. Moscow, 1957. (Translated from English.)
Finney, D. J. Vvedenie ν teoriiu planirovaniia eksperimentov. Moscow, 1970. (Translated from English.)
Fisher, R. A. Statisticheskie metody dlia issledovatelei. Moscow, 1958. (Translated from English.)
Hill, B. Osnovy meditsinskoi statistiki. Moscow, 1958. (Translated from English.)
Hicks, C. Osnovnye printsipy planirovaniia eksperimenta. Moscow, 1967. (Translated from English.)
Fisher, R. A. The Design of Experiments. Edinburgh-London, 1960.
N. V. GLOTOV, A. A. LIAPUNOV, and N. V. TIMOFEEV-RESOVSKII