Yes, as always.

are you need to known what is your decsion?

this is true if p

I say it depends on sample size. The Jarque–Bera test is comparing the shape of a given distribution (skewness and kurtosis) to that of a Normal distribution. I assume, like other Normality tests, as sample size increases you have a higher change of falling below the typical alpha value (i.e., 0.05; see Joris Meys illustration in link below).

If the test is being used to decide if the data will likely meet the assumptions of parametric tests, then one needs to consider that the central limit theorem usually renders the data "...sufficiently normal for the underlying assumption of normality to be reasonable for the practical purpose of the analysis..." (Joris Meys, comment in link below).

As a reminder, checks for Normality should be checked on the residuals of a model, because those assumptions apply to the unexplained variance of a model. Also note that the assumptions of independence, linearity, and heteroskedasticity can have more influence on the reliability of test than distribution assumptions, though highly skewed data can be just as problematic.

I think residual plots are better suited. Kozak and Piepho 2018 are much more in depth about checking Normality on raws vs. residuals and using tests or plots.

https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless

Article What's normal anyway? Residual plots are more telling than s...

Yes, the hypothesis is true.

Yes My Dear no any problem in your decision reject ofH0

Dear Victor

Your decision method is true but as we know JB test is not the most powerful test of normality. Usually AD, CVM and Shapiro-Wilks tests are better than JB test.

I suggest you, to make a good decision about normality, use more than one normality test and then make your final decision.

Good luck.

Yes this is right decision in test any Ho

yes your criteria is correct

You are correct, we reject the null that the residuals of a series are normally distributed when the probability associated with the JB test is significantly lower than the usual criterion of .05.

• Null hypothesis (H_0): The data is normally distributed.
• Alternate hypothesis (H_1): The data is not normally distributed, in other words, the departure from normality, as measured by the test statistic, is statistically significant.

kIndly posts the STATA commands for AD, CVM and Shapiro-Wilks tests for normality. I have tried the lowercase of AD and CVM but in vain.

Thank you

Kruskal-Wallis is better.

Usually, researchers make a grave mistake of stating that the data are normally distributed as the null hypothesis, this should actually stop, instead, what we test to be normal are the residuals of whatever variable you are interested in.

@Jose Risomar Sousa, Kruskal-Wallis isn't even a test for normality. Please stop posting all these short, irrelevant, or wrong answers. These kinds of responses do the opposite of the improving your reputation.