Any hypothesis one makes can be right or wrong, and it is necessary to test it. Due to the fact that the test is performed using statistical methods, it is called a statistical examination. As a result of statistical hypothesis testing, an incorrect decision may be made in two cases, and two types of errors may occur. Both errors cause adverse consequences, but their severity may differ from case to case.
First of all, it is necessary to define the different types of errors. An error of the first kind is that the correct hypothesis will be rejected. An error of the second kind is that an incorrect hypothesis will be accepted. It is necessary to emphasize that the consequences of these errors can be distinct (Emmert-Streib & Dehmer, 2019). For example, if the correct decision “to continue building the apartment building” is rejected, this first kind of error will cause material damage. If the wrong decision is made to “continue construction” despite the danger of a building collapse, then this mistake of the second kind can lead to loss of life. However, life situations can be different, and there are situations where a mistake of the first kind has more severe consequences than a mistake of the second kind.
Both of these characteristics are usually calculated with the help of the so-called power function of the criterion. In particular, the first kind of error probability is a power function calculated under the null hypothesis. For measures founded on a fixed-volume model, the second kind’s error likelihood is one minus the dominion function calculated under the premise that the issuance of statements conforms to the alternative hypothesis. (El-Gohary, 2019). For sequential criteria, this is also true if the criterion stops with probability one (for a given distribution from the alternative).
Thus, in statistical tests, one usually has to compromise between an acceptable level of errors of the first and second kinds. For example, in the case of a metal detector, increasing the sensitivity of the device will increase the risk of a first-order error (false alarm), and decreasing the sensitivity will increase the risk of a second-order error (missing a prohibited item). In conclusion, it is essential to note that the error severity level should be evaluated in each case.
References
El-Gohary, T. M. (2019). Hypothesis testing, type I and type II errors: Expert discussion with didactic clinical scenarios. International Journal of Health and Rehabilitation Sciences, 8(3), 132.
Emmert-Streib, F., & Dehmer, M. (2019). Understanding statistical hypothesis testing: The logic of statistical inference. Machine Learning and Knowledge Extraction, 1(3), 945-962. Web.