Szekessy Vilmos (szerk.): A Magyar Természettudományi Múzeum évkönyve 59. (Budapest 1967)

Berinkey, L.: The importance of statistical methods used in taxonomic investigations

ANNALES HISTORICO-NATURALES MUSEI NATIONALIS HUNGARICI Tomus 59. PARS ZOOLOGICA 1967. The Importance of Statistical Methods Used in Taxonomic Investigations By L. BERINKEY, Budapest The taxonomist has, in actual practice, no means to draw into his circle of study the entirety of the population (all of the constituent specimens) to be investigated; he has to rest content with the observing of a greater to smaller number of the respective specimens. This delimitation of the possibilities raises the question, however, in how far the taxonomist is justified and enabled in the drawing of conclusions, on the basis of the actually examined specimens, with respect to the entirety of the population, and what is the guarantee of the correctness of his inferences. If the solution of the given problem rests merely on the taxonomist's practice, powers of observation, exactitude, etc., a number of subjective sources of error will render the answer uncertain or doubtful. For the elimination of these subjective mistakes, the application of statistical mathematics in taxonomical studies submits its valuable help. According to the theory of mathematical statistics, the starting point of researches consists of observational data. The totality of these independent observational data, relating to the values of some random variable, is the sample. In taking a sample, one has to exercise the utmost care to exclude any distorting influence which would result in a false picture of the basic totality and its random fluctuations. If the sample answers this requirement, it is representative. In taxonomical investigations one must be careful that randomness be achieved and thus systematic effects obviated. In mathematical statistics, mathematical quantities, like arithmetic mean, standard deviation, distribution, etc., are defined as statistical functions, while their corresponding basic totality values as parameters. The most important statistical functions are as follows: 1. the mean of the sample, or the empiric mean; 2. the standard deviation of the sample; 3. the center of the sample ; 4. the range of the sample ; 5. the median of the sample; 6. the distribution function of the sample, or the empiric distribution function. Knowing these functions, one can infer on the parameters of the basic totality, and by their use execute further calculations. By the very nature of the taxonomist's work, they are rarely investigations of fitness, but rather those of deviations. In the followings, I intend to show, by using samples of three populations of Gobio gobio L. (the rivers Tapoly, Bükkös and Szamos), the importance of the application of statistical methods. In table 1, for the sake of a better survey and easier handling, the body height data of the three samples are arranged into statistical rows. Statistical rows may be true or untrue. True statistical rows are those in which the data are grouped according to an inner connection, with respect to size or order. The frequency rows of body height allow to establish the regularity of the rows.