Why has the Jarque-Bera test of normality two degrees of freedom?

My initial thought was that the sum of two squared standard normals (i.e., skewness and kurtosis in this test) should have n-1 = 2-1 = 1 df. So, why has it two?

Any help is very appreciated.

The test is described here: Wikipedia link

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#### Best Answer

"$chi^2$-distribution with $k$ degrees of freedom is the distribution of a sum of the squares of $k$ independent standard normal random variables" (Wikipedia: Chi-squared distribution)

So in the case of *Jarque-Bera test* the degrees of freedom must be 2, because – as you have stated – the test statistics is sum of two squared standard normally distributed values (skewness and kurtosis).