Testing of statistical hypotheses: general logic

Hypotheses are one of the most important factors in the development of science and the achievement of technical progress. Emerging as a result of observations of various phenomena and facts, the hypothesis is in its essence a theoretical assumption. In the course of an in-depth study of these facts and phenomena, it becomes necessary to test hypothetical assumptions. In this case, the methods used to test such assumptions must have a scientific justification. In other words, it is the result of observations or studies based on well-established scientific principles.

To determine the correctness of the theoretical assumption, there is a statistical test of hypotheses. This method involves the use of a statistical criterion that fits into a general logical scheme, consisting in finding a particular type of function according to the results of research or observations (critical statistics). Such a test of statistical hypotheses allows us to make a final decision on the correctness of the theoretical assumption.

The process of statistical analysis is often accompanied by the need to formulate and verify a certain theoretical assumption regarding the populations under study or the values of independent parameters. A comparison of the above assumption with the available data sampling, accompanied by an estimate of the degree of reliability of the derivation obtained and carried out using certain statistical criteria, is called a test of statistical hypotheses.

Statistical hypotheses should be understood as various kinds of theoretical assumptions about the nature and distribution parameters of certain random variables that can be tested, guided by the results of a random statistical sample. In other words, statistical hypotheses are the assumptions about the properties of general populations, for the verification of which one can use data from a statistical sample. Thus, it becomes possible to test the hypothesis of the equality of the average index of the general population and some hypothetical magnitude.

The verification of statistical hypotheses, the meaning of which is to confirm or reject, on the basis of available statistical data, a theoretical assumption with a minimal risk of making an error or error, is quite effective and in demand method of scientific research. The hypotheses are tested according to strictly defined rules.

It should always be remembered that the verification of statistical hypotheses is of a probabilistic nature. Using this method, you can determine in the digital (percentage) expression the probability of making the wrong decision or a false conclusion on the interpretation of the results of a statistical study of a phenomenon or event. If the probability of error or error is insignificant, the statistical regularities calculated in the study of the fact or phenomenon can be used for practical purposes with a slight risk of error.