
SIEGEL TUKEY TESTName:
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If LOWER TAILED is specified, a lower tailed test is performed (i.e., \( \sigma_1 \) < \( \sigma_2 \)). If UPPER TAILED is specified, an upper tailed test is performed (i.e., \( \sigma_1 \) > \( \sigma_2 \)). If neither LOWER TAILED or UPPER TAILED is specified, a twotailed test is performed (i.e., \( \sigma_1 \ne \sigma_2 \)).
<SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of two or more response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax performs all the twoway SiegelTukey tests for the listed variables. This syntax supports the TO syntax. If LOWER TAILED is specified, a lower tailed test is performed (i.e., \( \sigma_1 \) < \( \sigma_2 \)). If UPPER TAILED is specified, an upper tailed test is performed (i.e., \( \sigma_1 \) > \( \sigma_2 \)). If neither LOWER TAILED or UPPER TAILED is specified, a twotailed test is performed (i.e., \( \sigma_1 \ne \sigma_2 \)).
SIEGEL TUKEY TEST Y1 Y2 Y3 SIEGEL TUKEY TEST Y1 TO Y6 SIEGEL TUKEY TEST Y1 Y2 SUBSET Y2 > 0 LOWER TAILED SIEGEL TUKEY TEST Y1 Y2 UPPER TAILED SIEGEL TUKEY TEST Y1 Y2
LET STATCDF = SIEGEL TUKEY TEST CDF Y1 Y2 LET PVALUE = SIEGEL TUKEY TEST PVALUE Y1 Y2 LET PVALUE = SIEGEL TUKEY LOWER TAIL TEST PVALUE Y1 Y2 LET PVALUE = SIEGEL TUKEY UPPER TAIL TEST PVALUE Y1 Y2 In addition to the above LET commands, builtin statistics are supported for 30+ different commands (enter HELP STATISTICS for details).
. Step 1: Define the data (example from Higgin's book) . let y1 = data 16.55 15.36 15.94 16.43 16.01 let y2 = data 16.05 15.98 16.10 15.88 15.91 . . Step 2: Compute Siegel Tukey test statistic . let statva = siegel tukey test y1 y2 let statcdf = siegel tukey test cdf y1 y2 let pvalue = siegel tukey test pvalue y1 y2 . siegel tukey test y1 y2The following output is generated PARAMETERS AND CONSTANTS STATVA  24.00000 STATCDF  0.26543 PVALUE  0.53087 Two Sample TwoSided Siegel Tukey Test First Response Variable: Y1 Second Response Variable: Y2 H0: Sigma1 = Sigma2 Ha: Sigma1 not equal Sigma2 Summary Statistics: Number of Observations for Sample 1: 5 Mean for Sample 1: 16.05800 Median for Sample 1: 16.01000 Standard Deviation for Sample 1: 0.47007 Number of Observations for Sample 2: 5 Mean for Sample 2: 15.98400 Median for Sample 2: 15.98000 Standard Deviation for Sample 2: 0.09236 Test (Small Sample, Exact): Test Statistic Value: 24.00000 CDF Value: 0.26543 PValue (2tailed test): 0.53087 PValue (lowertailed test): 0.26543 PValue (uppertailed test): 1.00000 TwoTailed Test: Exact  Small Sample H0: F(x) = G(x); Ha: F(x) <> G(x) for some x  Lower Upper Null Significance Test Critical Critical Hypothesis Level Statistic Value (<) Value (>) Conclusion  80.0% 24.00000 21.00000 34.00000 ACCEPT 90.0% 24.00000 20.00000 35.00000 ACCEPT 95.0% 24.00000 18.00000 37.00000 ACCEPT 99.0% 24.00000 16.00000 39.00000 ACCEPT  
Date created: 07/17/2023 Last updated: 08/02/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 