
SKEWNESS OUTLIER TESTName:
The test statistic is the adjusted FisherPearson skewness coefficient
with n, \( \bar{x} \) and s denoting the sample size, the sample mean and the sample standard deviation, respectively. The critical values are obtained via simulation. The ASTM standard provides table values for n = 3 to 50 and \( \alpha \) levels of 0.10, 0.05 and 0.01. Linear interpolation is used for values of n not given in the table. Alternatively, you can perform a dynamic simulation to obtain the critical values. To specify the method used to compute the critical value, enter one of the following commands (the default is ASTM)
SET SKEW OUTLIER TEST CRITICAL VALUES SIMULATION If n > 50, the simulation method will be used.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable being tested; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of up to k response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax performs the skewness outlier test on <y1>, then on <y2>, and so on. Up to 30 response variables can be specified. Note that the syntax
is supported. This is equivalent to
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> ... <xk> is a list of up to k groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax performs a crosstabulation of <x1> ... <xk> and performs a skewness outlier test for each unique combination of crosstabulated values. For example, if X1 has 3 levels and X2 has 2 levels, there will be a total of 6 skewness outlier tests performed. Up to six groupid variables can be specified. Note that the syntax
is supported. This is equivalent to
MULTIPLE SKEWNESS OUTLIER TEST Y1 Y2 Y3 REPLICATED SKEWNESS OUTLIER TEST Y X1 X2 SKEWNESS OUTLIER TEST Y1 SUBSET TAG > 2
The STATCDF and PVALUE are only saved when the simulation method is used to obtain critical values. If the ASTM method is used to obtain critical values, the CUTOFF80 and CUTOF975 values are not saved. If the MULTIPLE or REPLICATED option is used, these values will be written to the file "dpst1f.dat" instead.
LET A = SKEWNESS OUTLIER TEST CDF Y LET A = SKEWNESS OUTLIER TEST PVALUE Y LET A = SKEWNESS OUTLIER TEST INDEX Y LET ALPHA = <value> LET A = SKEWNESS OUTLIER TEST CRITICAL VALUE Y The SKEWNESS OUTLIER TEST, SKEWNESS OUTLIER TEST CDF, and SKEWNESS OUTLIER TEST PVALUE return the values of the test statistic, the cdf of the test statistic and the pvalue of the test statistic, respectively. For the SKEWNESS OUTLIER TEST CDF and SKEWNESS OUTLIER TEST PVALUE commands, the simulation method will be used. Otherwise, the method specified by the SET SKEWNESS OUTLIER TEST CRITICAL VALUE command will be used. The SKEWNESS OUTLIER TEST INDEX returns the row index of the most extreme value in the response variable. The most extreme value is defined as the value furtherest from the mean. The SKEWNESS OUTLIER TEST CRITICAL VALUE returns the critical value for the specified value of ALPHA. If ALPHA is not specified, it will be set to 0.05. Note that if the ASTM method is specified for the critical values, only a few select values for alpha are supported (0.01, 0.05 and 0.10). In addition to the above LET command, builtin statistics are supported for 30+ different commands (enter HELP STATISTICS for details).
Ferguson, T.S. (1961), "On the Rejection of Outliers," Fourth Berkeley Symposium on Mathematical Statistics and Probability, edited by Jerzy Neyman, University of California Press, Berkeley and Los Angeles, CA. Ferguson, T.S. (1961), "Rules for Rejection of Outliers," Revue Inst. Int. de Stat., RINSA, Vol. 29, No. 3, pp. 2943.
. Step 1: Read the data (from ASTM E178 document) . read y 3.73 3.59 3.94 4.13 3.04 2.22 3.23 4.05 4.11 2.02 end of data set write decimals 3 . . Step 2: Compute the statistics . let stat = skew outlier test y set skew outlier test critical values astm let cv1 = skew outlier test critical value y set skew outlier test critical values simulation let cv2 = skew outlier test critical value y . let pval = skew outlier test pvalue y let statcdf = skew outlier test cdf y let iindx = skew outlier test index y . print stat cv1 cv2 pval statcdf iindx . set skew outlier test critical values astm skewness outlier test y set skew outlier test critical values simulation skewness outlier test yThe following output is generated PARAMETERS AND CONSTANTS STAT  0.969 CV1  1.131 CV2  1.139 PVAL  0.079 STATCDF  0.922 IINDX  10.000 THE FORTRAN COMMON CHARACTER VARIABLE SKEWOUTL HAS JUST BEEN SET TO ASTM Skewness Test for Outliers (Assumption: Normality) Response Variable: Y H0: The most extreme point is not an outlier Ha: The most extreme point is not an outlier Potential outlier value tested: 2.020 ID for potential outlier: 10 Summary Statistics: Number of Observations: 10 Sample Minimum: 2.020 Sample Maximum: 4.130 Sample Mean: 3.406 Sample SD: 0.771 Sample Adjusted Skewness: 0.969 Skewness Outlier Test Statistic Value: 0.969 Conclusions (Upper 1Tailed Test)  Alpha CDF Statistic Critical Value Conclusion  10% 90% 0.969 0.862 Accept H0 5% 95% 0.969 1.131 Reject H0 1% 99% 0.969 1.668 Reject H0 Critical Values Based on ASTM E178 Tables THE FORTRAN COMMON CHARACTER VARIABLE SKEWOUTL HAS JUST BEEN SET TO SIMU Skewness Test for Outliers (Assumption: Normality) Response Variable: Y H0: The most extreme point is not an outlier Ha: The most extreme point is not an outlier Potential outlier value tested: 2.020 ID for potential outlier: 10 Summary Statistics: Number of Observations: 10 Sample Minimum: 2.020 Sample Maximum: 4.130 Sample Mean: 3.406 Sample SD: 0.771 Sample Adjusted Skewness: 0.969 Skewness Outlier Test Statistic Value: 0.969 CDF Value: 0.923 PValue 0.077 Conclusions (Upper 1Tailed Test)  Alpha CDF Statistic Critical Value Conclusion  20% 80% 0.969 0.557 Accept H0 10% 90% 0.969 0.862 Accept H0 5% 95% 0.969 1.133 Reject H0 2.5% 97.5% 0.969 1.385 Reject H0 1% 99% 0.969 1.671 Reject H0 0.5% 99.5% 0.969 1.864 Reject H0 Critical Values Based on 50,000 Simulations  
Date created: 01/22/2020 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 