Sampling Method

SAMPLING METHOD, also called the representative method, the method of trials (Stichprobeerhebung, reprasentative Methode, laniethode representative, 1'investigation representative), is one of the methods of partial, non-entire statistical observation and research. The essence of the S. m. lies in the fact that a larger or smaller part of the cases of the studied phenomenon is selected and registered from the general mass of cases. Such a setting of research acquires essential significance in the following cases of statistical research practice: firstly, when the phenomenon of interest cannot be studied by means of an entire enumeration by its nature (as, for example, in the study of white and red balls in the blood, in the study of certain objects of the plant and animal worlds, etc.); secondly, when the latter cannot be applied due to a lack of forces, means, and time on the part of the researcher; thirdly, in those cases when, although there is a possibility to set up the research on the principles of an entire enumeration, at the same time it is obvious that such a setting would be devoid of practical sense, since the accuracy of the results obtained from an entire enumeration of observation units would differ little in a practical (but not theoretical) respect from the accuracy of the results obtained in a partial research. The data collected as a result of the S. m. differ from the data of an entire research in that they do not give a representation of the absolute number of units contained in the general aggregate of them; but with a correct setting of the selection, they give, to a greater or lesser extent, sufficient data for judgment on the internal structure of the studied mass and on its division into homogeneous constituent elements. The main moments determining the S. m. and distinguishing it from the two other methods of non-entire research—the questionnaire method and the monographic method—are the following two features: a) the S. m. represents a method of intentionally and consciously conducted non-entire, but nevertheless, massive statistical enumeration of cases of the studied phenomenon or selection from the total number of collected observations in an entire research, and b) in the S. m. a predetermined larger or smaller exactly established part of cases is registered or selected according to a special, also predetermined, method and a consistently carried out plan. Thus, the S. m. can be defined as "the method of intentionally partial massive statistical research, when the partial aggregate subject to observation is formed by the application of a certain, predetermined, system of selection, specially directed to the fact that, on the basis of the study of a part, a picture of the relationships of the whole is given" (V. Losievskaya). The S. m. differs from the questionnaire method in that in questionnaire research the non-entire volume in selection is a result of chance, a consequence of a kind of deviation from the planned entire research; in the S. m. the partial character of the data is obtained as a result of the conceived planned conduct of incomplete registration of research units. This difference, although technical, is in fact very significant, imprinting itself on the partial aggregates of observations obtained as a result of applying the questionnaire and S. m. methods. In contrast to the questionnaire method, the representative character of the aggregates created in the S. m. is ensured from the very beginning of the research in that the selection of observation units is carried out on the principles of chance in the sense of probability theory; this circumstance, in turn, leads to the fact that cases occurring in the studied mass in a larger number acquire more chances to fall into the sample aggregate, and cases occurring in it less frequently will have a smaller number of chances to enter the composition of the named aggregate. The sample aggregate is a reduced, in a certain, predetermined number of times, snapshot of the whole (Miniatttrbild); the partial aggregate in the questionnaire method is an unknown in its size and accuracy of transmission copy of the studied phenomenon. A direct consequence of the different content of the partial aggregates in the two considered methods is the difference in the possibility of their evaluation and use. In the latter respect, sample aggregates, being "mass" aggregates, built on a sufficient number of observations, and, under the condition of a correct setting of the selection technique, aggregates representing the general aggregate, allow transferring the properties characterizing them (summary characteristics, according to R. Orzhentsky) to the general aggregate. For the same reasons, sample aggregates can be constructed in a number of cases with a desirable degree of accuracy dictated by the tasks and goals of the research, and, conversely, sample aggregates obtained under given research conditions can be evaluated from the point of view of the degree of accuracy of the snapshot they transmit. The S. m. differs from the monographic method in that its basis is a mass, whereas in the monographic method the mass is unattainable by the very essence of the method. From what has been stated it is obvious that the selection technique and its size in the setting of the S. m. have essential significance. According to established practice, the selection technique can be carried out either purely mechanically or by the group method. In the mechanical way, the selection of units subject to registration or extraction from the general mass of records of an entire observation is carried out according to some purely random sign, but at the same time according to such a sign which is not included in the program of the sample research. The most frequently applied sign is the ordinal number or the alphabet. In the first case, from an entire list of observation objects or from the general mass of them (for example, from a list of peasant householders or from the general mass of general statistical cards compiled in outpatient clinics), those of them are selected which are listed in the list under certain numbers or are in the general mass under a certain ordinal number (for example, 5, 10, 15, etc., with a 20% selection). Besides the number, letters of the alphabet can be used as a selection sign. The essence of this selection system is based on the law of large numbers. However, for the law of large numbers to be able to manifest its influence, the selection must be carried out in a sufficiently large absolute number. Group selection consists in the fact that the studied mass is preliminarily divided into separate groups according to some determining its composition and state sign, and from the formed groups the units subject to observation are extracted mechanically. This type of selection, all other conditions being equal, is less reliable, since the establishment of groups is inseparably linked with the introduction by the researcher into the setting of research a certain share of subjectivism. But at the same time, group selection is necessary in the case of strong differentiation of the studied mass. The size of the selection, in constructing a sample research on the principles of mechanical selection and also under the condition that a given sample research was preceded by an entire research of the same phenomenon, can be built on the following formula: where a is the mean square error of frequency, p is frequency (the ratio of the absolute number of cases of the studied event—m—to the total number of the sample aggregate—n—), N is the number of the general aggregate and n is the number of the sample aggregate. Assigning to the results of the research the desired magnitude of accuracy (assuming, for example, that 2a^p (1_n~ ^p) (1 - |p) = 0.1 p at N= 150,000 and p = l%), it is not difficult to calculate the size of the selection (in this case it is equal to 20.4%). From the presented formula it is seen that the magnitude of the mean error depends to a considerable extent on the second part of the formula N-n. Changes in error in connection with changes in N are presented in the following form: n 1 " n n N' 0.5 0.0 0.81 0.1 3.00 0.7 0.65 0.2 2.00 0.8 0.50 0.3 1.53 0.9 0.33 0.4 1.22 1.0 0.00 0.5 1.00 In other words, with an increase of the sample from 10% to 20% the mean error decreases by two-thirds; if the sample is increased to 30%, then the mean error decreases, approximately, by half, etc. In addition, when establishing the size of the sample one should reckon with the absolute magnitude of the general aggregate, since the probable error of the mean decreases in a ratio inversely proportional to the square root of the number of units taken; with an increase of the number of observations by 4, 9, 25, etc. times, the reliability of the results increases only by 2, 3, 5, etc. times. Practically this means that with an increase of the general aggregate one can be satisfied with a relatively smaller sample aggregate. The practical significance of the S. m. follows, mainly, from the fact that it is a method of non-entire and a method of strictly statistical (based on the law of large numbers), its variety, and not a surrogate of the statistical method. With the application of the S. m. is connected the saving of forces, means, and time, which is especially valuable where the conduct of entire researches is impossible due to objective conditions (epidemics, famines, etc.).

In a number of questions, chiefly questions of a scientific nature, it is the only possible method, since for scientific generalizations it is essential to establish the common element present in the phenomena. This significance is connected with the origin of the Sampling Method. Its inventor was "statistical practice when it was forced to encounter tasks which proved insurmountable for a complete investigation" (Kauffman). The principles of the Sampling Method were first formulated by the Norwegian statistician Kiaer. The Sampling Method was repeatedly the subject of consideration at sessions of the International Statistical Institute (Bern-1895, St. Petersburg-1897, Budapest-1899, Berlin-1903, etc.). The said institute established the following point of view on it: "Recognizing that when properly applied the representative method, in certain cases, can give accurate and detailed observations, the results of which, with the observance of certain precautions, can be generalized, the institute recommends its application, drawing attention to the necessity of precisely indicating the conditions under which the observed units are selected" (Bulletin of the International Statistical Institute, Vol. XIV, Section 1, p. 133). In Russian statistical practice the Sampling Method found wide scope for application in agricultural research. From the first experiments of its use it is necessary to point out, chiefly, the following: the repeated investigation of Vyatka Governorate (1900-02, after the complete agricultural census carried out in the 80s), the investigation of peasant budgets in four districts of Kaluga Governorate (1896-97), the sampling investigation of Penza Governorate (1911-13), and the all-Russian agricultural census of 1916. In later times the Central Statistical Administration conducts annually a sampling spring investigation of peasant households and dynamic investigations of them. In 1928 the Sampling Method was first successfully applied for the investigation of the general morbidity of the population of the city of Moscow.