Any decision made based on a hypothesis test may be incorrect. In the
framework of hypothesis tests there are two types of errors: Type I error and type II error. A **type I
error** occurs when a true null hypothesis is rejected (a “false
positive”), while a **type II error** occurs when a false
null hypothesis is not rejected (a “false negative”). In other words, a
type I error is detecting an effect that is not present, while a type II
error is failing to detect an effect that is present.

\[ \begin{array}{l|ll} & H_0 \text{ is true} & H_0 \text{ is false} \\ \hline \text{Do not reject } H_0 & \text{Correct decision} & \text{Type II error} \\ \text{Reject } H_0 & \text{Type I error} & \text{Correct decision} \\ \hline \end{array} \]

If you are confused about type I and type II errors, you may find this illustration helpful (here).

Conducting a hypothesis test always implies, that there is a chance
of making an incorrect decision. The probability of the type I error (a
true null hypothesis is rejected) is commonly called the **significance level** of the
hypothesis test and is denoted by \(\alpha\). The probability of a type II
error (a false null hypothesis is not rejected) is denoted by \(\beta\). Keep in mind, that for a fixed
sample size the smaller we specify the significance level, \(\alpha\), the larger will be the
probability, \(\beta\), of not
rejecting a false null hypothesis.

The outcome of a hypothesis test is a statement in favor of the null
hypothesis or in favor of the alternative hypothesis. If the null
hypothesis is rejected, the data does provide sufficient evidence to
support the alternative hypothesis. If the null hypothesis is not
rejected, the data does not provide sufficient evidence to support the
alternative hypothesis. If the hypothesis test is performed at the
significance level \(\alpha\) and the
null hypothesis is rejected, one may state that the test results are
**statistically significant at the \(\alpha\) level**. If the null
hypothesis is not rejected at the significance level \(\alpha\), one may state that the test
results are **not statistically significant at the \(\alpha\) level**.

**Citation**

The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: *Hartmann,
K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis
using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.*