One of the basic concepts in statistics is the use mathematically rigorous tests to determine whether or not a researcher can reject their null hypothesis. The null hypothesis is the state of the world the researcher assumes exists. The alternative hypothesis is—as the name suggests—an alternative to the null hypothesis. Through these statistical tests, researchers try find the truth regarding a certain phenomenon. The degree of certainty the investigator has in his or her conclusion depends on the amount of type I and type II error in their calculations. Type I error occurs when the null is incorrectly rejected; type II error occurs when we fail to reject the null, when in fact the alternative is true. Below are more concrete examples of type I and type II errors.
In the criminal justice system, defendants are assumed to be innocent until proven guilty. Thus, the null hypothesis is that the individual is innocent while the alternative is that the defendant actually committed the crime. A type I error would occur if the individual was convicted of a crime they didn’t commit. A type II would presents itself when a guilty man is set free.
In the case of a clinical test for a new pharmaceutical, the null hypothesis would be that a new drug (drug N) is no better than the current drug (drug O). On the other hand, the alternative hypothesis would state that drug N is superior to drug O. A type I error would conclude that the new drug is better than the drug O, when in fact it is not. A type II error would conclude that the new and old pharmaceuticals are equivalent when in fact the drug N is superior.