🧪 The Jarque-Bera test

It is a statistical test used to test whether a sample of data comes from a normal distribution. It is based on the measure of skewness and kurtosis of the distribution.

How to Interpret It?

Null Hypothesis (H0): the data comes from a normal distribution.

The test calculates a test statistic (JB) that measures how much the measures of skewness and kurtosis of the data deviate from the expected values for a normal distribution (skewness = 0, kurtosis = 3).

Let's take an example: imagine that you want to test a new medicine. You want to know if this medicine is actually effective in treating a certain disease. To do this, you conduct a clinical trial and collect data.

The p-value associated with the JB statistic indicates the probability of obtaining a value of JB at least as large as the observed one, assuming that the null hypothesis is true.

If p-value < α (significance level, typically 0.05): the null hypothesis is rejected, concluding that the data does not follow a normal distribution.

If p-value ≥ α: there is not enough evidence to reject the null hypothesis.