A statistical hypothesis is a variant of possible regularities that obey the phenomenon under study. A simple statistical hypothesis determines the values of the parameters of a single probability distribution law or its form. A complex hypothesis is made up of many simple hypotheses.
Steps for testing statistical hypotheses
The essence of testing statistical hypotheses is to confirm or refute theoretical assumptions based on the obtained practical data and to minimize errors and errors. First, the object of study is presented in the form of a statistical hypothesis. Then its characteristics and the tested and alternative hypotheses are selected, taking into account the analysis of possible errors and their consequences.
The area of admissible values, the critical area, as well as the critical value of the statistical criterion are established. The actual value of the statistical criterion is calculated. The theoretical and practical values of the criterion are compared. The hypothesis is accepted or rejected according to the test results.
Statistical research analysis
When testing hypotheses according to one of the criteria, two erroneous decisions are possible - an error of the first kind: incorrect rejection of the null hypothesis and acceptance of an alternative one. Type II error: incorrectly accepting the null hypothesis instead of rejecting it. The formulation of an alternative hypothesis may vary. It all depends on which deviations from the value of the hypothesis are more important. It can be both positive and negative, or both.
The formulation determines the boundaries of the critical region, as well as the range of permissible values. The critical area is the area, falling of the study parameters into which leads to a deviation. The possibility of criterion parameters falling into this sphere is equal to the accepted level of significance.
If the obtained data fall into the range of permissible values, then the hypothesis put forward does not contradict the actual data and is not rejected. If the calculated value of the parameter falls into the critical region, then the null hypothesis contradicts the actual data and is rejected as a result. These areas are separated from each other by critical points or the boundaries of the critical area.
The border can be two-sided or one-sided, depending on how the alternative hypothesis is formulated. The statistical criterion establishes how much the hypothesis is consistent with the actual data, whether it can be left or must be rejected. Testing statistical hypotheses makes it possible to make a final decision about the accuracy of a hypothetical assumption.