# Tag Info

### What is the reason behind the name "adonis" (for permutational MANOVA)?

Actually it isn't -- the statistical method is not called adonis. The authors of the vegan software package for R (http://vegan.r-forge.r-project.org) implemented the statistical procedure you refer ...
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### Discriminant Function Analysis in SPSS: Sorts effectively, but Box's M is still 0.000. Is the analysis worthless?

Box's M test is to check if the groups' covariances matrices are the same in the population; this homogeneity of covariances is as assumption of linear discriminant analysis (LDA). The test is quite ...
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### Why does MANOVA report values of F-statistic in addition to Pillai/Wilks/Hotelling/Roy?

The primary test statistics are the four values given: Pillai's trace, Wilks' lambda, Hotelling's trace and Roy's largest root. The distribution of each of these is, in general, complicated and so ...
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### How to interpret type I, type II, and type III ANOVA and MANOVA?

For illustration I assume a two dimensional ANOVA model specified by y ~ A * B Type I ANOVA Line term in ANOVA table Hypothesis from model Hypothesis to model A y~...
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### What is the reason behind the name "adonis" (for permutational MANOVA)?

I am the culprit and this is my true confession: it was Hank's idea (Martin Henry H. Stevens). We already had a function called anosim (Analysis of Similarities, of Primer strain) in vegan, and even ...
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### How is MANOVA a case of the GLM?

Just as t-tests and ANOVAs are special cases of the univariate general linear model (as you show in your question), the univariate general linear model is also just a special case of the full general ...
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### MANOVA as protection against Type I errors

Requiring a significant MANOVA or ANOVA before conducting individual t-tests can help protect against Type I error, but is not generally sufficient to provide strong Type I error control. For example, ...
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### What is the explanation of the difference caused by the order of variables in anova for the concrete example in R?

When you call anova on an lm model fit, under the hood you are really using ?anova.lm, which ...
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### MANOVA with variables from different datasets

One option here is to think of this as a missing data problem. You have varying amounts of information for each case (different tree species) that you have classified as one of five different species. ...
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### Is it okay to perform PerMANOVA on PCA values?

I will leave it to others to decide if a permutational multivariate analysis of variance on principal components is 'acceptable' to them. But there isn't any logical error in computing such a ...
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### What analysis is best with a binary independent variable that is very skewed?

This is not an issue at all and your analysis should not change based on the distribution of this variable. A regression model with event, your moderator, and their interaction would be sufficient. I ...
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### Why is it rarely reported in papers which type of sums of squares is used in Anova results?

This is not an easy question to answer (at least for me) but my guess is that the great majority of people go with the default settings of the program that they are using (irrespective of whether this ...
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### Why is Pillai's trace equal to partial eta squared in a repeated measures MANOVA (profile analysis)?

The short answer to your question is... ... in a multivariate context, there is much less of a distinction between hypothesis test statistics (e.g. F in a univariate context) and effect size ...
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### Should I use MANOVA, ANOVA for Regression?

It sounds more like a multiple regression question. All three of MANOVA, ANOVA, and regression fit into the heading of the general linear model. ANOVA is a special case of the linear model where you ...

### Within-Subjects or Between-Subjects MANOVA

The error term will typically be lower when between-subjects variance is removed from error as it is in within-subject designs but not in between-subjects designs. As is often said: subjects are their ...
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### A is correlated with B/ A has an impact on B

Counterexample: Acne causes kids to start middle school. No...they simply happen to coincide because both occur around the time kids are 10-12 and therefore starting middle school. This is true for ...
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### Is this a proper use of mixed modeling?

The model you are thinking about: Area ~ Peptide + ( Peptide | Reaction_Time ) doesn't really make sense. The primary interest is in the association of reaction ...
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### Treat year as a fixed effect, random effect, or covariate?

First note that including a variable as a covariate and as a fixed effect means exactly the same thing to the model. So the question is about whether to include year as a fixed or a random effect. I ...
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### Replicating an SPSS manova in R

I am not very familiar with SPSS but as far as I see MANOVA in SPSS reports multivariate tests for each predictor separately (just like manova in R). So, it does ...
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### If data is square rooted to assume normality, should the data used to test with Levene's Test for Equality of Variance also be square rooted?

If you do the equality of variance test for the purposes of assumptions of manova, you need to test the data on the scale you will use in the manova. Presumably (after what you told us) that is the ...
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### Excluding participants due to issue in randomisation?

Equal group size is not a requirement for anova (it might be an advantage if you can have it). So, as long as group assignment is still random and representative, as you say it is, there is no reason ...
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### Significant output in Levene's test for equality of variances in MANOVA; what to do?

First, make sure you look at the boxplots of the residuals instead of just using Levene's tests. The significant result could be due to outliers, a bimodal distribution, or skewness that you may need ...

### Does one need to adjust for multiple comparisons when using MANOVA?

There's no need to adjust the alpha level of the MANOVA test itself, as amoeba noted. However, a significant MANOVA doesn't allow you to make statements about any of your 10 DVs--that would require ...
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### Transformations possible when performing a single multivariate ANOVA on a continuous and categorical species database?

For the record, after discussions with other colleagues, I believe since my species in categories (from 0 = absence to 4 = 75-100% cover) are somewhat already transformed, the best way will be square ...
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### Pros and cons of 5 ANOVAs for 5 DVs instead of 1 MANOVA

It depends on what the research question is. Multivariate analyses help to answer the question "Is there a main effect on any of these DVs?". So, if there's no theory-driven prediction on any ...
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### Repeated measures analysis of mutually correlated features

You might consider a repeated-measures MANOVA. The MANOVA is analogous to the ANOVA, but with more than one dependent variable. Just like the ANOVA, you can have several independent variables (...
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### What is the explanation of the difference caused by the order of variables in anova for the concrete example in R?

I like to understand linear regression in terms of its computation. A linear model is computed by QR factorization, giving a number of "effects" on the rotated plane. You can refer to What is the “...
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### Why is Pillai's trace equal to partial eta squared in a repeated measures MANOVA (profile analysis)?

Let - considering MANOVA with one factor with $k$ groups, for simplicity - $\bf B$ be the between-groups scatter matrix and $\bf W$ be the pooled within-group scatter matrix. (Please see "Bonus" ...
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