I try to compare the output from permanova (run in PrimerE) and adonis (in R) on the same dataset. SS, MS, and F are identical. However, I am getting more and more confused about the terms "estimated variance components" (ECV) and "explained variance" (R-square ?). adonis outputs R-square as SSfactor/SStotal (which is sometimes also called eta-square (η2) in a regular anova). As this statistic is somewhat biased, omega-square (ω2) is sometimes calculated, but this is another story. However, looking at the permanova output and the explanations in the manual, the story seems to be much more complex. permanova estimates the components of variation in the model using the mean squares. If I understand correctly, the square-root of these ECV are then directly related to the explained variance and percent explained variance is derived by getting the proportions of the total (=sum). There has been a post on researchgate on this (https://www.researchgate.net/post/Can_you_report_PERMANOVA_estimated_components_of_variation_ECV_as_a_proportion_of_variation_explained_by_factors_terms), but it didn't really solve that issue, did it?
Can someone help to explain the differences between ECV and explained variance and the way permanova and adonis is handlig these differently? Any guidance is greatly appreciated.
Dear Martin Hartmann
To compare the outputs of Permanova versus adonis, you can perform equality of mean test (Using Z-test when population variance is known or otherwise t-test) with one tail or two tail test. For equality of variance, you can perform F test. There is different between estimated variance components" (ECV) and "explained variance" (R-square. Estimated variance is the variance after regression estimation and explained variation is how much variation of the devendent variable is explained by the independent variables.
I hope you get the answer.
Dear Ahammad. Thanks for your response. Nevertheless, the two approaches define the "explained variance" differently. Whereas permanova calculates it through the ECV, adonis uses SSfactor/SStotal.
See also the discussion here: https://www.researchgate.net/post/Can_you_report_PERMANOVA_estimated_components_of_variation_ECV_as_a_proportion_of_variation_explained_by_factors_terms.
Having said this, the difference is still not clear to me.
Best wishes, Martin
Hi, I am trying to solve the same issue that you had 3 years ago and still I was not really able to find an answer to it. Did you ever find out what the difference is and how to calculate ECV using adonis in R? I checked all the papers cited in the other post which recommend to calculate ratio ø =(estimated magnitude of variance for each factor)/(estimated residual variance). I tried different calculations with the output from R but I am still not sure how to calculate it. So if you have new insights about this I would be really happy to hear them.
Best wishes
Martine
Hi! I have the same problem, and Im not sure if estimates of components of variation outputted by permanova can really be converted into percentages... I guess i can add the values and then calculate the proportion of each source, but I dont really know if interpretate the components of variation as a percentage of how much a factor affects a dependent variable is correct...
Hi Martin,
You are right, their is no satisfactory answer to this.
I also realized that quite recently that "adonis" is returning "r2" that are based on SS and not MS, which is I think more preferable, as it readjusts the variance estimates based on degree of freedom. Also getting into the art of model nesting and "strata" use can be of interest, but then its gets quickly confusing. At least I see the variance where it should be that way using the MS% (e.g. batch, generation effects...) while the SS% gives very funny results sometimes depending where you have your degree of freedom and how you have invested them when building your model.
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