26 Apr 2011

Adonis (PERMANOVA) - Assumptions

Before you use PERMANOVA (R-vegan function adonis) you should read the user notes for the original program by the author (Marti J. Anderson) who first came up with this method. An important assumtption for PERMANOVA is same "multivariate spread" among groups, which is similar to variance homogeneity in univariate ANOVA.

I'll show why you may draw the wrong conclusions if this assumption is not met:


# two similar populations:

# generating a third sample from the same population, but with reduced
# number of species occurrences. this set will have higher
# beta-diversity (or "multivariate spread"):

# distance matrices:

# when computing sets with same beta-dispersion we get a
# correct adonis result with no sign. group differences
# in species composition:

# when using sets with different beta-diversity you may
# get false significant adonis results - the location/composition
# is actually the same (!) this result is due to different
# multivariate spread in dat1 and dat2:

# see ordination diagram where location (centroids) between dat1 and dat2
# is not shifted more than for dat1a dat1b, still you yield a (false)
# sign. adonis result
# plot:


main="same beta-disp\nsame location")

main="diff beta-disp\nsame location")



  1. What is the alternative then?

    1. I'd still do the Permanova but report that there is a considerable difference in multivariate spread that either could be the cause for the significant Permanova result. Of course, there are lots of other multivariate methods that could be considered, but I guess that's beyond the scope of this posting..

  2. Dear Kay,

    Is it advisable to use adonis as a nonparametric alternative for Two-Way Anova?



    1. Hi Fernando,

      I think there's a range of other statistical tools to be used for the analysis of univariate data. I'd advise you to post to an appropiate mailing list, describing your problem in detail and providing some toy-data.


    2. Dear Kay,

      Below is my dataset. We are testing surfaces for cell attachment, the surfaces are made combining two modifications at the beginning with two at the ending of the process.
      The response variable is not normal, so I turned to use adonis to analyze the data. My knowledge of statistic is very basic (college level) and mainly with parametric tests, I have found that some discussions caution against the use of adonis, so I am wondering if use it to analyse my data is correct. Also, I want to do multiple comparisons tests after, could I use Tukey for it?

      All the best, and thanks for any help

      Treatment ModInit ModTer cells/mm2
      ABS alfa-89 M3 60.92
      ABS alfa-89 M3 28.96
      ABS alfa-89 M3 26.68
      ABS alfa-89 M3 29.02
      ICA GusX M3 70.12
      ICA GusX M3 73
      ICA GusX M3 79.93
      ICA GusX M3 66.32
      OEA alfa-89 98-L 67.27
      OEA alfa-89 98-L 66.59
      OEA alfa-89 98-L 72.11
      OEA alfa-89 98-L 69.1
      ZZM GusX 98-L 62.75
      ZZM GusX 98-L 37.76
      ZZM GusX 98-L 57.01
      ZZM GusX 98-L 73.28

    3. Fernando,

      You're barking up the wrong tree - PERMANOVA is unsuited for your (univariate) data - it is designed to fit multivariate data! There are other statistical methods which should be considered here. Just google for "alternative two-way anova".. When you have decided upon a test and aren't sure about the results, post to r-help for advise.


  3. It will be great if anyone can tell me urgently please how to create the experimental design file and the data file for the PERMANOVA program.
    My data are representing the temporal macrofaunal abundance response towards both the months and the species.
    I've read the manual the following paragraph

    ((A. Design file The first file the program requires is the design file. This file contains all of the information that the program needs regarding the factors in the experimental design, whether they are fixed or random, crossed (orthogonal) or nested in one another. The file is very easily created by hand in a text editor (such as “Notepad” or “SimpleText”). It should be saved as an ASCII text (*.txt) file. The design file contains the following information:
    1. In the first line is given an integer, which is the number of factors
    2. Next, a line is given for each factor in the design, in the order that they occur in the data file, providing the following information separated by tabs:
    a. the name of the factor;
    b. the number of levels of the factor;
    c. whether the factor is crossed (“C”) or nested (“N”) in some other factor(s);
    d. whether the factor is fixed (“F”) or random (“R”);
    e. if the factor is nested, then the number(s) corresponding to the factor(s) within which it is nested must be listed, with no spaces or tabs in between these numbers. If the factor is not nested, then a zero is given here (“0”).
    3. The last line contains the number of replicate observation units per cell (sample size, n). ))

    but I don't know how to construct the files for PERMANOVA especially how to deal with the dependent factor which is the macrofaunal abundance.

    I'm looking forward to hearing from you please
    My e-mail is:
    many thanks

    1. Sorry pal, I'm afraid you're addressing the wrong person! My advise: go to the PERMANOVA web-site, read the manuals & if that doesn't suffice, consider to contact the program mantainer.


    2. Can you provide link to the PERMANOVA web site please?

    3. ..Google? 3rd hit: http://www.stat.auckland.ac.nz/~mja/Programs.htm

  4. Please help me urgently! Can I run PERMANOVA in R on unbalanced design? Thank you in advance.


  5. Hi Kay,
    I was just wondering if you had come across any ways of analyzing repeated measures data with adonis. I'm sure it can be done but haven't a clue as to how.

    1. Yes, it can be done - check http://thebiobucket.blogspot.com/2011/04/repeat-measure-adonis-lately-i-had-to.html

  6. You can in-fact use PERMANOVA as a non-parametric univariate test. When you set the distance measure to Euclidean and have a design that uses unconstrained permutations, PERMANOVA provides nearly identical results to a one-way ANOVA. The only assumption is independence of samples since dispersion is a non-issue in univariate data. You also beat the normality assumption. Beware, the model syntax in R doesn't handle complex experimental designs, but for a one-way or two-way design, you should be fine. See the original PERMANOVA manuscript in Austral Ecology. Here is a paper that uses and explains how PERMANOVA can be used on univariate data: http://www.researchgate.net/publication/233389938_Enhancing_Garry_oak_seedling_performance_in_a_semiarid_environment

  7. Hi Kay,

    Great work!! My colleagues and I are trying to make sense of some biological data tested with a PERMANOVA. The PERMANOVA experts ran the test, but an issue remains unsolved: should the data be homoscedastic (i.e., should variances be quasi-identical, or the "multivariate spread" be similar between groups) to apply a PERMANOVA? We seem to get contrasting answers (including from the scientific literature), and have been unable to move on. Your analysis strongly suggests that data indeed should be homoscedastic (or multivariate equivalent) to apply a PERMANOVA.

    What do you suggest to fix the problem of (slight) heteroscedasticity for our data? How can we quote you? Our research is going to be published in a scientific journal, so we need as exact and "hard" a citation as possible (I'm afraid that a blog quotation won't do it...).

    Please be gentle with me, as I'm not the PERMANOVA expert in this endeavor of ours.... Though I will forward your reply to the PERMANOVA expert of our group. We're all ecologists and nobody is a real statistician, so please don't get too technical. If you prefer I can you my e-mail address.

    Thanks a lot, and kudos for your blog!!


    PS: Thanks also to the blog commentators.

  8. Thank you!

    Just consult the PERMANOVA User Notes!.. Marti Anderson: "[...] Although there is also no explicit assumption regarding the homogeneity of spread within each group, PERMANOVA, like ANOSIM (Clarke 1993), will be sensitive to differences in spread (variability) among groups. Thus, if a significant difference between groups is detected using PERMANOVA, then this could be due to differences in location, differences in spread, or a combination of the two. Perhaps the best approach is to perform a separate test for homogeneity (e.g., using the program PERMDISP) including pair-wisecomparisons, as well as examining the average within and between-group distances and associated MDS plots. This will help to determine the nature of the difference between any pair of groups, whether it be due to location, spread, or a combination of the two. [...]"

    This says it all!

    In a publication I would just report that a slight difference in multivariate spread was observed and that this might contribute to the effects observed.. Depending of the result of the appropiate PERMDISP tests I would judge about the relevance of difference in multivariate spread..

    Good Luck,

    For citation use the ones given in the User Notes for PERMANOVA by Marti Anderson (see link in OP).

    1. Hi Kay,

      Thanks a lot for your advice!!! We have solved our problem, and your comment was pivotal in tipping the balance toward the "right" size.

      Sorry for not having replied any sooner, just got extra-extra-busy while the real PERMANOVA experts were working on the problem, then I had experienced a little computer problem of my own. Everything is fine now -- thanks again!!!