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Standard errors of skewness and kurtosis are all the same for a set of variables

Troubleshooting


Problem

I'm running the SPSS EXAMINE procedure (Analyze>Descriptive Statistics>Explore in the menus) using a number of dependent variables. Among the descriptive statistics produced are skewness, kurtosis and their standard errors. I've noticed that the standard errors for these two statistics are the same for all of my variables, regardless of the values of the skewness and kurtosis statistics. Is something wrong?

Resolving The Problem

No, there is nothing wrong here. The standard errors for skewness and kurtosis are solely functions of the sample size, regardless of the values of the statistics themselves. EXAMINE uses LISTWISE deletion of cases with missing values by default, so for a given group, descriptive statistics for all variables will be based on the same number of cases. Thus the SEs for skewness and kurtosis will be the same for all variables.

The variance (squared standard error) of the skewness statistic is computed as:

V_skew = 6*N*(N-1) / ((N-2)*(N+1)*(N+3))

where N is the sample size. The variance of the kurtosis statistic is:

V_kur = 4*(N^2-1)*V_skew / ((N-3)*(N+5))

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Historical Number

78312

Document Information

Modified date:
16 April 2020

UID

swg21481716

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