Jarque-Bera test
Goodness of fit and normality · reference distribution: χ²(2)
When to use it
Test normality through skewness and kurtosis; common in econometrics, with large samples.
Null hypothesis
Zero skewness and kurtosis of 3, as in the normal.
Assumptions
- Large samples: in small samples the test is unreliable
Test statistic
JB = \dfrac{n}{6}\left(S^2 + \dfrac{(K - 3)^2}{4}\right)How to report it
JB = 3.1, p = .21
In R and Python
R
library(tseries)
jarque.bera.test(x)Python
stats.jarque_bera(x)In Python, stats is scipy.stats and np is numpy.
Where it sits in the catalog
Goodness of fit and normality. Goodness of fit: do the data follow the expected distribution? Normality tests are the most common case and check an assumption of parametric tests.
In the decision tree
- What do you want to do? Check an assumption or the distribution of the data
- What do you want to check? Whether the data are normal
- How large is the sample? Large, as in econometrics