Tne nestedRanksTest package provides functions for performing a Mann-Whitney-Wilcoxon-type nonparametric test for a difference between treatment levels using nested ranks, together with functions for displaying results of the test. The nested ranks test may be used when observations are structured into several groups and each group has received both treatment levels. The p-value is determined via bootstrapping.

The nestedRanksTest is intended to be one possible mixed-model extension of the Mann-Whitney-Wilcoxon test, for which treatment is a fixed effect and group membership is a random effect. The standard Mann-Whitney-Wilcoxon test is available in R as wilcox.test.

The latest stable release of the package can be downloaded from CRAN:


Help is available via ?nestedRanksTest, and a vignette is available via:


The development version is hosted on github and can be installed via:

devtools::install_github("douglasgscofield/nestedRanksTest", build_vignettes = TRUE)

These statistical tools were developed in collaboration with Peter E. Smouse (Rutgers University) and Victoria L. Sork (UCLA) and were funded in part by U.S. National Science Foundation awards NSF-DEB-0514956 and NSF-DEB-0516529.

To Use It

The principle function is nestedRanksTest(), with two interfaces. The formula interface is the simplest to use. It allows specification of quantitative measures, treatments and group membership using R's familiar formula syntax. Treat group membership as a random factor or grouping variable by using "|":

result <- nestedRanksTest(Distance ~ Year | Granary, data = woodpecker_multiyear,
                          subset = Species == "agrifolia")

    Nested Ranks Test

data:  Distance by Year grouped by Granary
Z = 0.27695, p-value = 1e-04
alternative hypothesis: Z lies above bootstrapped null values
null values:
      0%       1%       5%      10%      25%      50%      75%      90%      95%
-0.29492 -0.15583 -0.11059 -0.08705 -0.04554 -0.00124  0.04430  0.08488  0.10936
     99%     100% 
 0.15335  0.27695 

bootstrap iterations: 10000 
group weights:
        10         31        140        151        152        938        942 
0.05204461 0.04646840 0.02478315 0.14560099 0.30359356 0.29120198 0.13630731 

nestedRanksTest plot example

The default interface uses arguments for specifying the variables.

# Make variables accessible using with()
result <- with(subset(woodpecker_multiyear, Species == "agrifolia"),
               nestedRanksTest(y = Distance, x = Year, groups = Granary))


The statistic for the nested ranks test is a Z-score calculated by comparing ranks between treatment levels, with contributions of each group to the final Z-score weighted by group size. The p-value is determined by comparing the observed Z-score against a distribution of Z-scores calculated by bootstrapping ranks assuming no influence of treatment while respecting group sizes. When there is just one group, this test is essentially identical to a standard Mann-Whitney-Wilcoxon test.

For further details, please see the vignette for this package:



The generation of a null distribution can take some time. For example, if any use of nestedRanksTest() in the examples were run with the default n.iter = 10000, completion would require a few seconds.

Return value

nestedRanksTest() returns a list of class 'htest_boot' based on class 'htest' containing the following components. Components marked with * are additions to 'htest'.

Component | Contents ----------|---------- statistic | the value of the observed Z-score. p.value | the p-value for the test. alternative | a character string describing the alternative hypothesis. method | a character string indicating the nested ranks test performed. | a character string giving the name(s) of the data.. bad.obs | the number of observations in the data excluded because of NA values. null.values | quantiles of the null distribution used for calculating the p-value. n.iter* | the number of bootstrap iterations used for generating the null distribution. weights* | the weights for groups, calculated by nestedRanksTest_weights. null.distribution* | vector containing null distribution of Z-scores, with statistic the last value.

The length of null.distribution equals n.iter. Note that null.distribution will not be present if the lightweight = TRUE option was given to nestedRanksTest.


The package also includes a dataset, woodpecker_multiyear, which contains the data on woodpecker acorn movement underlying Figure 2 in Thompson et al. (2014).


Thompson PG, Smouse PE, Scofield DG, Sork VL. 2014. What seeds tell us about birds: a multi-year analysis of acorn woodpecker foraging movements. Movement Ecology 2: 12, Open Access

douglasgscofield/nestedRanksTest documentation built on May 13, 2017, 4:38 a.m.