Why do I get this p-value doing the Jarque-Bera test in R?

Doing a Jarque Bera test in R I get this result:

jarque.bera.test(rnorm(85))

data:  rnorm(85)

X-squared = 1.259, df = 2, p-value = 0.5329

Does it mean that the probability to discard the normality hypothesis (it being true) is 53.29%?

If so, why do I get this value if I used a random number from a normal distribution?

Answer

p-value = 0.5329

Does it mean that the probability to discard the normality hypothesis

A p-value is not “the probability to discard the hypothesis”. You should review the meaning of p-values. The first sentence of the relevant wikipedia page should help:

the p-value is the probability of obtaining the observed sample results (or a more extreme result) when the null hypothesis is actually true.

(NB: I have modified the above link to the version that was current at the time I wrote the answer, as the opening paragraph of the article has been edited badly and it’s presently – June 2018 – effectively wrong.)

It goes on to say:

If this p-value is very small, usually less than or equal to a threshold value previously chosen called the significance level (traditionally 5% or 1% [1]), it suggests that the observed data is inconsistent with the assumption that the null hypothesis is true

This is quite different from “probability to discard the hypothesis”.

is 53.29%?

A p-value around 53% is quite consistent with the null hypothesis.

(However, this does not imply that the distribution that the data were supposedly a random sample from is normal; it would be consistent with an infinite number of non-normal distributions as well.)

Attribution
Source : Link , Question Author : will198 , Answer Author : Community

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