Définition Statistical hypothesis testing

Statistical hypothesis testing (also 'confirmatory data analysis') is used in inferential statistics to either confirm or falsify a hypothesis based on empirical observations.

An example:

It is assumed, that people in the US, over time, are getting older (on average). In this case, the hypothesis to be confirmed is: 'the average age of people in the US is rising'. This is called the alternative hypothesis, whereas the current opinion 'the average age of people in the US stays the same' is called the null hypothesis. The goal of a statistical test would be to either verify of falsify the alternative hypothesis.

This is where it gets complicated:

In hypothesis testing, we differentiate between parametric and non-parametric tests.

In parametric tests we compare location and dispersion parameters of two samples and check for compliance. Examples for parametric tests are the t-test, f-test and the χ2-test.

In nonparametric tests on the other hand, no assumptions about probability distributions of the population which is being assessed are being made. Examples are the Kolmogorov-Smirnov test, the chi-square test and the Shapiro-Wilk test.

Performing hypothesis tests:

In order to perform statistical hypothesis testings, we first have to collect the according empirical data (for example: age reached of 100 people, born in 1900 and 1920 respectively). Depending on the hypothesis made and the resulting test procedure, a mathematically defined test statistic (f-statistic, t-statistic, …) is deducted from the observed data.

Based on this value, we can determine whether the null hypothesis can be rejected or not – accounting for a specified rate of reliability (1- error probability). The null hypothesis should only be rejected based on a very low probability of error (p≤5%).

Since errors when verifying or falsifying hypotheses cannot be generally excluded, errors of the first kind (=a true null hypothesis is incorrectly rejected, also: type I error) and errors of the second kind (= a true alternative hypothesis is incorrectly rejected, also: type II errors) are usually explicitly specified.