Jarque-Bera Test: Chi-Square Distribution Table

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SUMMARY

The Jarque-Bera test statistic follows a chi-square distribution with two degrees of freedom, which is used to assess the null hypothesis that a dataset is normally distributed. At a 0.05 confidence interval, the critical value from the Chi-Square Distribution Table is 5.99. If the Jarque-Bera test statistic exceeds 5.99, the null hypothesis of normality is rejected, indicating significant skewness or excess kurtosis in the data. This conclusion is supported by the relationship between the JB statistic and the expected values of skewness and excess kurtosis for normal distributions.

PREREQUISITES
  • Understanding of the Jarque-Bera test and its application in statistical analysis.
  • Familiarity with chi-square distribution and its significance levels.
  • Knowledge of skewness and excess kurtosis in the context of normality testing.
  • Basic statistical hypothesis testing concepts.
NEXT STEPS
  • Study the derivation and assumptions of the Jarque-Bera test.
  • Learn about alternative tests for normality, such as the Shapiro-Wilk test.
  • Explore the implications of skewness and kurtosis in data analysis.
  • Review statistical software options for performing the Jarque-Bera test, such as R or Python's SciPy library.
USEFUL FOR

Statisticians, data analysts, and researchers involved in hypothesis testing and normality assessment in their datasets.

kimberley
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Hi all.

Wikipedia states:

"The [Jarque-Bera] statistic has an asymptotic chi-square distribution with two degrees of freedom and can be used to test the null hypothesis that the data are from a normal distribution. The null hypothesis is a joint hypothesis of both the skewness and excess kurtosis being 0, since samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0. As the definition of JB shows, any deviation from this increases the JB statistic."

When I look at the Chi-Square Distribution Table at the .05 confidence interval, it returns the number 5.99. Out of an abundance of caution, does this mean that if my Jarque-Bera test statistic is greater than 5.99, that the null hypothesis of normality is rejected? This would seem to be correct since the JB statistic is usually only greater than 5.99 if the skew and excess kurtosis are relatively far from 0, and the JB statistic tends to be closer to 1 or less than 1 when skew and excess kurtosis are close to 0. Thank you in advance.

Kim
 
Physics news on Phys.org
That would be correct.
 
Thanks Again Enuma

EnumaElish said:
That would be correct.


Much appreciated.
 

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