Jarque-Bera Test: Chi-Square Distribution Table

In summary, the Jarque-Bera statistic is a test for the null hypothesis that data are from a normal distribution. If the test statistic is greater than 5.99, the null hypothesis of normality is rejected. This is because the JB statistic is typically only greater than 5.99 when the skew and excess kurtosis are far from 0.
  • #1
kimberley
14
0
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
 
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  • #2
That would be correct.
 
  • #3
Thanks Again Enuma

EnumaElish said:
That would be correct.


Much appreciated.
 

FAQ: Jarque-Bera Test: Chi-Square Distribution Table

What is the Jarque-Bera Test?

The Jarque-Bera Test is a statistical test used to determine whether a given data set follows a normal distribution or not. It is based on the skewness and kurtosis of the data, and uses the Chi-Square Distribution Table to calculate the p-value.

Why is the Chi-Square Distribution Table used in the Jarque-Bera Test?

The Chi-Square Distribution Table is used in the Jarque-Bera Test because it allows for the calculation of the p-value, which is used to determine the significance of the test results. The p-value is compared to a predetermined significance level, usually 0.05, to determine whether the data follows a normal distribution or not.

How do I interpret the results of the Jarque-Bera Test?

If the p-value is greater than the significance level, then the data is considered to be normally distributed. However, if the p-value is less than the significance level, then the data is not considered to be normally distributed.

What is skewness and kurtosis?

Skewness is a measure of the asymmetry of a data set. A perfectly symmetric data set will have a skewness of 0. Positive skewness indicates that the data is skewed to the right, while negative skewness indicates that the data is skewed to the left.

Kurtosis is a measure of the peakedness of a data set. A data set with a normal distribution will have a kurtosis of 3. If the kurtosis is greater than 3, the data is more peaked than a normal distribution, and if it is less than 3, the data is less peaked than a normal distribution.

What are the assumptions of the Jarque-Bera Test?

The Jarque-Bera Test assumes that the data is independent, random, and normally distributed. It also assumes that the sample size is large enough to provide accurate results. Violation of these assumptions may lead to inaccurate results and conclusions.

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