**Inferential statistics** is all about making decisions
or judgments about the value of a particular observation or measurement.
One of the most commonly used methods for making such decisions is to
perform a hypothesis test. A hypothesis is a proposed explanation for a
phenomenon. In the context of statistical hypothesis tests the term
hypothesis is a statement about something that is supposed to be
true.

A hypothesis test involves two hypotheses: the **null
hypothesis** and the **alternative hypothesis**. The
null hypothesis \((H_0)\) is a
statement to be tested. The alternative hypothesis \((H_A)\) is a statement that is considered
to be an alternative to the null hypothesis.

The hypothesis test is aimed to test if the null hypothesis should be rejected in favor of the alternative hypothesis. The basic logic of a hypothesis test is to compare two statistical data sets. One data set is obtained by sampling and the other data set originates from an idealized model. If the sample data is consistent with the idealized model, the null hypothesis is not rejected. If the sample data is inconsistent with the idealized model and thus supports an alternative hypothesis, the null hypothesis is rejected in favor of the alternative hypothesis.

The criterion for deciding whether to reject the null hypothesis
involves a so called **test statistic**. The test statistic
is a number calculated from the data set, which is obtained by
measurements and observations, or more general by sampling.

**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.*