
SIGNED RANK TESTName:
The signed rank test is also commonly called the Wilcoxon signed rank test or simply the Wilcoxon test. To form the signed rank test, compute d_{i} = X_{i}  Y_{i} where X and Y are the two samples. Rank the d_{i} without regard to sign. Tied values are not included in the Wilcoxon test. After ranking, restore the sign (plus or minus) to the ranks. Then compute W+ and W as the sums of the positive and negative ranks respectively. If the two population means are in fact equal, then the sums of the ranks should also be nearly equal. If the difference between the sum of the ranks is too great, we reject the null hypothesis that the population means are equal.
Significance levels are based on the fact that if there
is no difference in the population means, then there
are 2 More formally, the hypothesis test is defined as follows.
Although the above discussion was in terms of a paired two sample test, it can easily be adapted to the following additional cases:
where <y1> is a response variable; <mu> is a number or parameter that is the hypothesized mean value; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax implements the one sample signed rank test.
where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax implements the two sample paired signed rank test where the hypothesized difference between the population means for the two samples is zero.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <mu> is a number or parameter that is the hypothesized difference between the means of the two samples; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax implements the two sample paired signed rank test where the hypothesized difference between the population means for the two samples is equal to a nonzero value.
SIGNED RANK TEST Y1 Y2 SIGNED RANK TEST Y1 Y2 MU SIGNED RANK TEST Y1 Y2 SUBSET TAG > 2
STATCD2 = the normal cdf value of W CUTLOW90 = 0.05 critical value CUTUPP90 = 0.95 critical value CUTLOW95 = 0.025 critical value CUTUPP95 = 0.975 critical value CUTLOW99 = 0.005 critical value CUTUPP99 = 0.995 critical value Note that the above critical values are the lower and upper tails for two sided tests (i.e., each tail is alpha/2. For example, CUTLOW90 is the lower 5% of the normal percent point function (adjusted for the mean and standard deviation). This is the critical regions for alpha = 0.10, so there is 0.05 in each tail.
WILCOXON SIGNED RANK WILCOXON SIGN TEST WILCOXON TEST SIGNED RANK
READ NATR332.DAT Y1 Y2 SIGNED RANK TEST Y1 Y2 The following output is generated. WILCOXON SIGNED RANK TEST (PAIRED 2SAMPLE) HYPOTHESIS BEING TESTINGPOPULATION MEANS MU1 = MU2 SAMPLE SIZE = 10 NUMBER OF NONZERO DIFFERENCES = 7 SUM OF POSITIVE RANKS (W+) = 13.50000 SUM OF NEGATIVE RANKS (W) = 14.50000 WILCOXON SIGNED RANK TEST STATITIC (W) = 13.50000 HYPOTHESIS ACCEPTANCE INTERVAL CONCLUSION MU1 < MU2 W > 4.000000 ACCEPT MU1 = MU2 W > 2.000000 ACCEPT MU1 > MU2 W+ > 4.000000 ACCEPT
Date created: 6/5/2001 