Wilcoxon Signed Rank Test for Paired-Samples

Advanced Statistics > Nonparametric Analysis > Two Wilcoxon

Performs Wilcoxon Signed Rank Test for Paired-Samples.

The Wilcoxon signed rank test for paired-samples is used to test whether two paired sets of observations come from the same distribution. The alternative hypothesis is that the observations come from distributions with identical shape but different locations. Unlike the two-sampled t-test this test does not assume that the observations come from normal distributions.

The assumptions for this are:

The paired differences (Di)are mutually independent.

Each paired difference (Di) comes from a continuous distribution that is symmetric, with the same center of symmetry. Strictly speaking, the population distributions need not be the same for all the paired differences. However, if we want a consistent test, we assume that the paired differences all come from the same continuous, symmetric distribution.

The paired differences all have the same median. Moreover, since the mean of a continuous symmetric distribution is equal to its median, this means that the paired differences will also all have the same mean.

In most situations you should use a two-sided test. A two sided test is based upon the null hypothesis that the common median of the differences is zero. The approximate alternative hypothesis in this case is that the differences tend not to be zero. For a lower-sided test the approximate alternative hypothesis is that differences tend to be less than zero. For an upper-sided test the approximate alternative hypothesis is that that differences tend to be greater than zero.


Dialog box items

Samples in different columns: Choose if the data of the two samples are in separate columns.

First Sample: Enter the column containing one sample.

Second Sample: Enter the column containing the other sample

Samples in one column: Choose if the sample data are in a single column, differentiated by factor levels in a second column.

Samples: Enter the columns containing the sample data.

Factor and Levels: Enter the columns containing the sample factor, and select the levels.


The display of outputs of VisualStat.



Data can be entered in one of two ways:

Both samples in a single numeric column with another grouping column (called factor) to identify the population. The grouping column may be categorical, numeric or text.

Each sample in a separate numeric column.

Each row contains the paired measurements for an observation. Paired observations where one of values is missing are ignored.



Test median: Enter the null hypothesis test value.

Alternative Hypothesis: Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level: Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.



Whitley and Ball reported data on the central venous oxygen saturation (SvO2 (%)) from 10 consecutive patients at 2 time points; at admission and 6 hours after admission to the intensive care unit (ICU). The null hypothesis is that there is no effect of 6 hours of ICU treatment on SvO2. Under the null hypothesis, the mean of the differences between SvO2 at admission and that at 6 hours after admission should be zero.

1.Open the DataBook nonparam.vstz

2.Select the sheet oxygen

3.Choose the tab Advanced Statistics, the group Nonparametric Tests and the command Two Wilcoxon

4.Select group Samples in different columns

5.In First Sample, select On Admission. In Second Sample, select At 6 Hours.

6.Click OK


Report window output


Wilcoxon Signed Rank Test for Paired-Samples


Test of median = 0 versus median not = 0

alternative hypothesis: true median of paired differences is not equal to 0


              On Admission - At 6 Hours

N              10

Expected diff  0.0000

Mean Rank      -4.5000

Rank Sum       -45.0000

Z Statistic    -2.2934

Distribution   Normal Approximation

p-value        0.0218

alpha-level    0.05

Z Critical     1.9600

Conclusion     Accept the Alternative Hypothesis

              i.e. the median of paired differences between `On Admission´ and `At 6 Hours´

              is significantly different from the expected value at the 5% level.

              in another word, test of median of `On Admission´ - `At 6 Hours´ = 0 vs

              median of `On Admission´ - `At 6 Hours´ <> 0 is significant at 0.05




See Also:

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