
SKEWNESSName:
where \(\bar{x}\), s, and n are the sample mean, the sample standard deviation, and the sample size, respectively. Note that in computing the skewness, the standard deviation is computed using n in the denominator rather than n  1. The adjusted FisherPearson skewness coefficient is:
This provides a correction factor to adjust for the sample size. This adjustment factor approaches 1 as the sample size gets large. In Dataplot, you can specify that the adjusted form of the statistic be computed by entering the command
To reset the unadjusted skewness statistic, enter
There are many alternative definitions of skewness in the literature. Dataplot supports the following two additional definitions of skewness. The Galton skewness (also known as Bowley's skewness) is defined as
The Pearson 2 skewness coefficient is defined as
where <y> is the response variable; <par> is a parameter where the skewness is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the FisherPearson skewness.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the skewness is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the Galton skewness.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the skewness is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the Pearson two skewness.
LET A = GALTON SKEWNESS Y1 LET A = PEARSON TWO SKEWNESS Y1 LET A = SKEWNESS Y1 SUBSET Y1 > 0
Measurement data is often bounded below (e.g., the measurement must be positive) but not above. This type of data will frequently exhibit right skewness.
STANDARDIZED 3RD CENTRAL MOMENT PEARSON 2 SKEWNESS PEARSON TYPE TWO SKEWNESS PEARSON TYPE 2 SKEWNESS
2013/04: Added adjusted FisherPearson skewness 2014/12: Added Galton skewness 2014/12: Added Pearson two skewness skip 25 read weibbury.dat y . let s1 = skewness y set skewness definition adjusted fisher pearson let s2 = skewness y let s3 = galton skewness y let s4 = pearson two skewness y . set write decimals 4 print s1 s2 s3 s4The following output is generated PARAMETERS AND CONSTANTS S1  0.0329 S2  0.0356 S3  0.2280 S4  0.4449  
Date created: 12/14/2014 Last updated: 11/01/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 