
TWO SAMPLE PERMUATION TESTName:
The NITER computed statistics represent the reference distribution. The statistic for the original data is compared to this reference distribution. For example, the cutoffs for a 95% twosided test are obtained from the 2.5% and 97.5% percentiles of the reference distribution. The permutation test is based on all possible permutations of the data. However, the number of permutations ((n1+n2)!/(n1!n2!)) grows rapidly as the sample sizes increase. However, sampling a subset of all possible permutations provides a reasonable approximation for the permutation test. By default, Dataplot generates 4,000 iterations. To change this, enter the command
If <value> is less than 100, it will be set to 100. If <value> is greater than 100,000, it will be set to 100,000. The specified statistic should be one that can be computed from a single response variable (e.g., MEAN, MEDIAN, VARIANCE). By default, Dataplot will compute the difference of the statistic between the two samples. For scale statistics (e.g., STANDARD DEVIATION, VARIANCE), it is often preferred to compute the ratio rather than the difference. To specify the ratio be computed, enter
To reset the default, enter
Permutation tests assume the observations are independent. However, no distributional assumptions are made about the response variables.
<y1> <y2> <SUBSET/EXCEPT/FOR qualification> where <stat> is the desired statistic; <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. If UPPER TAILED is specified, an upper tailed test is performed. If neither LOWER TAILED or UPPER TAILED is specified, a twotailed test is performed. To see a list of supported statistics, enter HELP STATISTICS.
PERMUATION TEST <y1> ... <yk> <SUBSET/EXCEPT/FOR qualification> where <stat> is the desired statistic; <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 two sample permutation tests for the listed variables. This syntax supports the TO syntax. If LOWER TAILED is specified, a lower tailed test is performed. If UPPER TAILED is specified, an upper tailed test is performed. If neither LOWER TAILED or UPPER TAILED is specified, a twotailed test is performed. To see a list of supported statistics, enter HELP STATISTICS.
TWO SAMPLE MEDIAN PERMUATION TEST Y1 Y2 TWO SAMPLE MEDIAN PERMUATION TEST Y1 Y2 SUBSET Y2 > 0 LOWER TAILED TWO SAMPLE MEDIAN PERMUATION TEST Y1 Y2 UPPER TAILED TWO SAMPLE MEDIAN PERMUATION TEST Y1 Y2
SET PERMUTATION TEST RATIO
Knuth (1998), "The Art of Computer Programming: Volume 2 Seminumerical Algorithms, Third Edition", Section 3.4.2, AddisonWesley. Knoble RANDPERM algorithm downloaded from: "http://coding.derkeiler.com/Archive/Fortran/comp.lang.fortran/ 200603/msg00748.html"
set random number generator fibbonacci congruential seed 32119 . . Read the data . skip 25 read auto83b.dat y1 y2 retain y2 subset y2 >= 0 . . Perform the permutation test . lower tailed two sample mean permutation test y1 y2 upper tailed two sample mean permutation test y1 y2 two sample mean permutation test y1 y2 . . Plot the results . title offset 7 title case asis label case asis y1label Count x1label Difference of Means for Permutations let statval = round(statval,3) let p025 = round(p025,3) let p975 = round(p975,3) let pval = round(pvalue2t,3) let statcdf = round(statcdf,3) . x2label color red x2label Difference of Means for Original Sample: ^statval x3label color blue x3label 2.5 Percentile: ^P025, 97.5 Percentile: ^P975 xlimits 0.5 0.5 let niter = 4000 skip 1 read dpst1f.dat z title Histogram of Difference of Means for ^niter Permutationscr() ... (Pvalue: ^pval, CDF: ^statcdf) . histogram z . line color red line dash drawdsds statval 20 statval 90 line color blue line dash drawdsds p025 20 p025 90 drawdsds p975 20 p975 90The following output is generated Two Sample Permutation Test (Difference) MEAN First Response Variable: Y1 Second Response Variable: Y2 H0: Difference = 0 Ha: Difference < 0 Sample One Summary Statistics: Number of Observations: 249 Sample Mean: 20.14458 Sample Median: 19.00000 Sample Standard Deviation: 6.41470 Sample Two Summary Statistics: Number of Observations: 79 Sample Mean: 30.48101 Sample Median: 32.00000 Sample Standard Deviation: 6.10771 Test: Number of Permutation Samples: 4000 Statistic Value: 10.33643 Test CDF Value: 0.00000 Test PValue: 0.00000 Conclusions (Lower 1Tailed Test)  Null Significance Test Critical Hypothesis Level Statistic Region (<=) Conclusion  80.0% 10.33643 0.83209 REJECT 90.0% 10.33643 1.29897 REJECT 95.0% 10.33643 1.63245 REJECT 99.0% 10.33643 2.38263 REJECT Two Sample Permutation Test (Difference) MEAN First Response Variable: Y1 Second Response Variable: Y2 H0: Difference = 0 Ha: Difference > 0 Sample One Summary Statistics: Number of Observations: 249 Sample Mean: 20.14458 Sample Median: 19.00000 Sample Standard Deviation: 6.41470 Sample Two Summary Statistics: Number of Observations: 79 Sample Mean: 30.48101 Sample Median: 32.00000 Sample Standard Deviation: 6.10771 Test: Number of Permutation Samples: 4000 Statistic Value: 10.33643 Test CDF Value: 0.00000 Test PValue: 1.00000 Conclusions (Upper 1Tailed Test)  Null Significance Test Critical Hypothesis Level Statistic Region (>=) Conclusion  80.0% 10.33643 0.85202 ACCEPT 90.0% 10.33643 1.30055 ACCEPT 95.0% 10.33643 1.65238 ACCEPT 99.0% 10.33643 2.36938 ACCEPT Two Sample Permutation Test (Difference) MEAN First Response Variable: Y1 Second Response Variable: Y2 H0: Difference = 0 Ha: Difference not equal 0 Sample One Summary Statistics: Number of Observations: 249 Sample Mean: 20.14458 Sample Median: 19.00000 Sample Standard Deviation: 6.41470 Sample Two Summary Statistics: Number of Observations: 79 Sample Mean: 30.48101 Sample Median: 32.00000 Sample Standard Deviation: 6.10771 Test: Number of Permutation Samples: 4000 Statistic Value: 10.33643 Test CDF Value: 0.00000 Test PValue: 0.00000 Conclusions (TwoTailed Test)  Null Significance Test Critical Critical Hypothesis Level Statistic Region (<=) Region (>=) Conclusion  80.0% 10.33643 1.33232 1.28555 REJECT 90.0% 10.33643 1.69915 1.63487 REJECT 95.0% 10.33643 1.99929 1.90250 REJECT 99.0% 10.33643 2.64950 2.60265 REJECT  
Date created: 08/04/2023 Last updated: 09/25/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 