# Type II Error - Definition

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### Type II Error Definition

A type II error occurs when there is a non-rejection of a false null hypothesis, this type of error is also called a false negative finding or conclusion. In statistical hypothesis testing, if a false null hypothesis is not rejected when it should have been, a type II error has occurred. In this type of error, a false null hypothesis is accepted while a true null hypothesis is rejected. Type 1 error and type II error often go hand in hand because when certain steps are taken to reduce the occurrence of a type II error, the probability of a type I error occurring increases.

### A Little More on What is Type II Error

A type II error occurs when there is non-rejection of a false null hypothesis and a rejection of an alternative hypothesis that did not occur due to chance. This type of hypothesis testing error accepts an item or idea that should have been rejected and reject an alternative hypothesis even if it is true. A type II error is otherwise called a beta error, this type of error confirms a false finding as true. There are certain ways to reduce type II error but this could also create an increase in Type 1 error. Type I error occurs when a true null hypothesis is rejected. Here are some crucial points to know about a type II error;

• A type II error occurs in hypothesis testing when a null hypothesis that is false is confirmed or incorrectly retained.
• The non-rejection of a false null hypothesis and the rejection of an alternative hypothesis, even though it did not happen by chance.
• A type II error is a false positive error, which can be reduced by taking certain steps.
• A reduction in type II error could lead to an increase in type I error, this is why analysts often consider the probability of these errors before conducting a hypothesis test.

### Differences Between Type I and Type II Errors

There is a clear difference between a Type I error and a type II error, analysts that conduct hypothesis tests need to take cognizance of these errors and the probability that they might occur in a test. A type I error rejects a null hypothesis when it is true while a type II error does not reject a null hypothesis when it is false. The probability of committing a type I error and a type II error in a hypothesis test differs, for instance, the probability of committing a type I error equals the level of significance set for the test while that of type II error is equal to 1 minus the power of the test.

### Academic research for Type II Error

Type I and Type II error concerns in fMRI research: re-balancing the scale, Lieberman, M. D., & Cunningham, W. A. (2009). Type I and Type II error concerns in fMRI research: re-balancing the scale. Social cognitive and affective neuroscience, 4(4), 423-428. The importance of beta, the type II error and sample size in the design and interpretation of the randomized control trial: Survey of 71 negative trials, Freiman, J. A., Chalmers, T. C., Smith Jr, H., & Kuebler, R. R. (1978). The importance of beta, the type II error and sample size in the design and interpretation of the randomized control trial: Survey of 71 negative trials. New England Journal of Medicine, 299(13), 690-694. A more realistic look at the robustness and type II error properties of the t test to departures from population normality., Sawilowsky, S. S., & Blair, R. C. (1992). A more realistic look at the robustness and type II error properties of the t test to departures from population normality. Psychological bulletin, 111(2), 352. Type I and type II error rates for quantitative trait loci (QTL) mapping studies using recombinant inbred mouse strains, Belknap, J. K., Mitchell, S. R., O'Toole, L. A., Helms, M. L., & Crabbe, J. C. (1996). Type I and type II error rates for quantitative trait loci (QTL) mapping studies using recombinant inbred mouse strains. Behavior genetics, 26(2), 149-160. Power, precaution, Type II error and sampling design in assessment of environmental impacts, Underwood, A. J., & Chapman, M. G. (2003). Power, precaution, Type II error and sampling design in assessment of environmental impacts. Journal of Experimental Marine Biology and Ecology, 296(1), 49-70. Type-II error rates (beta errors) of randomized trials in orthopaedic trauma, Lochner, H. V., Bhandari, M., & Tornetta III, P. (2001). Type-II error rates (beta errors) of randomized trials in orthopaedic trauma. JBJS, 83(11), 1650-1655. Type I and type II error under randomeffects misspecification in generalized linear mixed models, Litire, S., Alonso, A., & Molenberghs, G. (2007). Type I and type II error under randomeffects misspecification in generalized linear mixed models. Biometrics, 63(4), 1038-1044. Type I Error, Type II Error, and the Private Securities Litigation Reform Act, Stout, L. A. (1996). Type I Error, Type II Error, and the Private Securities Litigation Reform Act. Ariz. L. Rev., 38, 711. Nonlinearity, multicollinearity and the probability of type II error in detecting interaction, Ganzach, Y. (1998). Nonlinearity, multicollinearity and the probability of type II error in detecting interaction. Journal of Management, 24(5), 615-622. Type II error problems in the use of moderated multiple regression for the detection of moderating effects of dichotomous variables, Stone-Romero, E. F., Alliger, G. M., & Aguinis, H. (1994). Type II error problems in the use of moderated multiple regression for the detection of moderating effects of dichotomous variables. Journal of Management, 20(1), 167-178.