
Wilcoxon Rank Sum procedure demonstrated with an exampleThe Wilcoxon rankrum test (Wilcoxon MannWhiney Utest, or WMW test)A common experiment design is to have a test and control conditions. A two sample ttest would have been a good choice if the test and control groups are independent and follow Normal distribution. If conditions are not met, nonparametric test methods are needed. This section covers one such test, called Wilcoxon ranksum test (equivalent to the MannWhiney Utest) for two samples. The test is preferred when:
Analyzing the data with WMW testConsider the following example. Soil respiration is a measure of Microbioal activity in soil, which affects plant growth. In one study, soil cores were taken from two locations in a forest: 1) under an opening in the forest canopy (the "gap"location) and 2) at a nearby area under heavy tree growth (the "growth" location). The amount of carbon dioxide given off by each soil core was measured (in mol CO_{2}/g soio/hr). The question is to test whether the gap and growth areas do not differ with respect to soil respiration. The model can be set up as: Soil respiration(continuous) ~ location group (categorical: 2 levels) The data is "soil.csv". Open the data set from SAS. Or import with the following command. data soil; infile "H:\sas\data\soil.csv" dlm=',' firstobs=2; input group $ resp; run; According to the Normality check of the data, the distributions does not appear Normal. Hence, a WMW test is run with the following command. proc NPAR1WAY data=soil wilcoxon; title "Nonparametric test to compare respiration between growth and gap area"; class group; var resp; exact wilcoxon; run; The SAS procedure NPAR1WAY performs the non parametric tests. The option "wilcoxon" requests the Wilcoson rank sum test (plus a number of other statistics). The "class" and "var" statements are identical to the same statements of the ttest procedure. The "exact" statement causes the program to compute exact pvalues (in addition to the asymptotic approximations usually computed) for the tests listed after this statement. It is suggested that an "exact" statement is included when the sample size is relatively small. Output and intepretationNonparametric test to compare respiration between growth and gap area The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable resp Classified by Variable group Sum of Expected Std Dev Mean group N Scores Under H0 Under H0 Score  growth 7 77.50 56.0 8.625543 11.071429 gap 8 42.50 64.0 8.625543 5.312500 Average scores were used for ties. Wilcoxon TwoSample Test Statistic (S) 77.5000 Normal Approximation Z 2.4346 OneSided Pr > Z 0.0075 TwoSided Pr > Z 0.0149 t Approximation OneSided Pr > Z 0.0144 TwoSided Pr > Z 0.0289 Exact Test OneSided Pr >= S 0.0051 TwoSided Pr >= S  Mean 0.0099 Z includes a continuity correction of 0.5. KruskalWallis Test ChiSquare 6.2130 DF 1 Pr > ChiSquare 0.0127 For WMW test, the most critical output is from the Exact test, as repeated below, Exact Test OneSided Pr >= S 0.0051 TwoSided Pr >= S  Mean 0.0099 Therefore, the pvalue =0.0099 (<0.05) for a twosided (nondirectional)test, since pvalue is less than 0.05 we conclude that the the respiration between growth and gap areas are significantly different.

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