Hypothesis testing in statistics involves deciding whether to reject or not reject a null hypothesis. There are problems that can occur when making decisions about a null hypothesis. A researcher can reject a null when they should not reject it, which is called a type I error. The other mistake is not rejecting a null when they should have, which is a type II error. Both of these mistakes represent can seriously damage the interpretation of data.
The classic example that explains type I and type II errors is a courtroom. In a trial, the defendant is considered innocent until proven guilty. The defendant can be compared to the null hypothesis being true. The prosecutor job is to present evidence that the defendant is guilty. This is the same as providing statistical evidence to reject the null hypothesis which indicates that the null is not true and needs to be rejected.
There are four possible outcomes of our trial and our statistical test…
- The defendant can be declared guilty when they are really guilty. That’s a correct decision.This is the same as rejecting the null hypothesis.
- The defendant could be judged not guilty when they really are innocent. That’s a correct and is the same as not rejecting the null hypothesis.
- The defendant is convicted when they are actually innocent, which is wrong. This is the same as rejecting the null hypothesis when you should not and is know as a type I error
- The defendant is guilty but declared innocent, which is also incorrect. This is the same as not rejecting the null hypothesis when you should have. This is known as a type II error.
The probability of committing a type I error is the same as the alpha or significance level of a statistical test. Common values associated with alpha are o.1, 0.05, and 0.01. This means that the likelihood of committing a type I error depends on the level of the significance that the researcher picks.
The probability of committing a type II error is known as beta. Calculating beta is complicated as you need specific values in your null and alternative hypothesis. It is not always possible to supply this. As such, researcher often do not focus on type II error avoidance as they do with type I.
Another concern is that decrease the risk of committing one type of error increases the risk of committing the other. This means that if you reduce the risk of type I error you increase the risk of committing a type II error.
The risk of error or incorrect judgment of a null hypothesis is a risk in statistical analysis. As such, researchers need to be aware of these problems as they study data.