
JARQUE BERA TESTName:
The JarqueBera test statistic is defined as:
with S, K, and N denoting the sample skewness, the sample kurtosis, and the sample size, respectively. For sample sizes of 2,000 or larger, this test statistic is compared to a chisquared distribution with 2 degrees of freedom (normality is rejected if the test statistic is greater than the chisquared value). The chisquare approximation requires fairly large sample sizes to be accurate. For sample sizes less than 2,000, the critical value is determined via simulation. Specifically, one hundred thousand normal samples with the same mean and standard deviation as the original data sample are generated and the JarqueBera test statistic computed to generate the reference distribution.
where <y> is the response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> is a list of 1 to 6 groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
JARQUE BERA TEST Y1 SUBSET TAG > 2 MULTIPLE JARQUE BERA TEST Y1 TO Y10 REPLICATED JARQUE BERA TEST Y X
For Syntax 3 (the REPLICATED form), the variables must all have the same number of observations.
LET A = JARQUE BERA TEST CDF Y LET A = JARQUE BERA TEST PVALUE Y In addition to the above LET command, builtin statistics are supported for about 20+ different commands (enter HELP STATISTICS for details).
JARQUE BERA
SKIP 25 READ ZARR13.DAT Y1 READ ZARR15.DAT Y2 SET WRITE DECIMALS 4 MULTIPLE JARQUE BERA TEST Y1 Y2The following output is generated JarqueBera Test for Normality Response Variable: Y1 H0: The Data Are Normally Distributed Ha: The Data Are Not Normally Distributed Summary Statistics: Total Number of Observations: 195 Sample Mean: 9.2614 Sample Standard Deviation: 0.0227 Sample Skewness: 0.0085 Sample Kurtosis: 3.0490 Sample Minimum: 9.1968 Sample Maximum: 9.3279 Test Statistic Value: 0.0219 CDF Value: 0.0101 PValue: 0.9898 Percent Points of the Reference Distribution  Percent Point Value  25.0 = 0.553 50.0 = 1.256 75.0 = 2.403 80.0 = 2.774 90.0 = 4.044 95.0 = 5.679 97.5 = 8.034 99.0 = 12.567 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 4.044 Accept H0 5% 95% 5.679 Accept H0 2.5% 97.5% 8.034 Accept H0 1% 99% 12.567 Accept H0 JarqueBera Test for Normality Response Variable: Y2 H0: The Data Are Normally Distributed Ha: The Data Are Not Normally Distributed Summary Statistics: Total Number of Observations: 211 Sample Mean: 9.2772 Sample Standard Deviation: 0.1117 Sample Skewness: 0.0067 Sample Kurtosis: 2.4502 Sample Minimum: 9.0274 Sample Maximum: 9.5219 Test Statistic Value: 2.6585 CDF Value: 0.7840 PValue: 0.2159 Percent Points of the Reference Distribution  Percent Point Value  25.0 = 0.557 50.0 = 1.266 75.0 = 2.415 80.0 = 2.786 90.0 = 4.084 95.0 = 5.718 97.5 = 8.066 99.0 = 12.467 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 4.084 Accept H0 5% 95% 5.718 Accept H0 2.5% 97.5% 8.066 Accept H0 1% 99% 12.467 Accept H0  
Date created: 07/05/2012 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 