Hello Guilherme,

Do you mean that a pair of your dependent variables is highly correlated? That, by itself, doesn't make manova inappropriate.

Of course, you should assure that the two DVs in question are genuinely distinct, and not merely replicates of each other. For example, if we measured the stature of participants twice, once using a rule calibrated in cm, and a second time using a furlong-length rule that was calibrated in 1/8ths of a furlong. You'd expect the correlation between the two scores to be high, but not perfect due to human error in interpolating measured height. However, they are both the same variable.

Good luck with your work.

David Morse, I a a bit puzzled by the warning you gave about ensuring that the DVs are genuinely distinct, and by the example you gave. Your comments seem (to me) to be at odds with the use of MANOVA to analyze repeated measures designs (as one way of dealing with violation of sphericity). In that case, repeated measures of the same variable (under different conditions or at different times) are treated as if they are distinct outcome variables. Does that concern you? Thanks for clarifying. (And of course, we both know that nowadays, multilevel modelling of repeated measures is generally preferred to both classical RM ANOVA and to the multivariate approach.)

Bruce

Since your DVs seem highly correlated, you might consider why you regarded them as separate variables! Interestingly, the claims that correlations alone contribute to the effectiveness of MANOVA are simply “myths” (Frane, 2015).

Frane, A. V. (2015). Power and type I error control for univariate comparisons in multivariate two-group designs. Multivariate Behavioral Research, 50(2), 233–247. https://doi.org/10.1080/00273171.2014.968836

Good luck,

My dearest friend Bruce after discarding several examples I have come to this. There is a difference between measuring the same expemental unit multiple times and measuring multiple units in exactly the same way..this is the confusing because of the language but what you and Dr Morse are . considering is different but not the same thing.lol. That's why ANOVA IMO can be more confusing than regression so let's dump ANOVA and do regression now that we don't have calculations by hand any more. That was Fisher's original intent I believe. So hang in Dr Morse and make SPSS people go to a less confusing human language to explain things like most of the users have done. Got that everyone,? Remember a regression model is simply more simple than one from an ANOVA would suggest.. Good luck with your stats courses but TG I learned regression first. Best wishes to all and to all a good day. David Booth. BTW SPSS is fine but the associated language is

so confusingg that most people are easily confused as is my message today. Where's Andy Field when we need him?. oops there.

Good morning David Eugene Booth. I'm afraid that your post confuses me even more than David Morse's post.

You wrote: "There is a difference between measuring the same expemental unit multiple times and measuring multiple units in exactly the same way."

I am very well aware of that, but fail to see what it has to do with the questions I put to David Morse. Perhaps I need to back up and give more context for my questions to him.

When any repeated measures factor has more than 2 levels, one of the key assumptions of classical RM ANOVA is sphericity. As Thom Baguley notes in his blog post on sphericity (see link below), there have been two general approaches to dealing with violations of sphericity: 1) Using a method that corrects for it (e.g., Greenhouse-Geisser), or 2) Using MANOVA. The latter approach treats the repeated measurements (on the same individuals) of the same DV as if they are distinct outcome variables.

• http://psychologicalstatistics.blogspot.com/2006/05/what-is-all-this-stuff-about.html

David M gave an example of measuring stature twice for each individual, but using two different methods. That, in my mind, is an example of "repeated measures"--i.e., measuring the same DV more than once on the same individuals. But as noted above, one way to analyze repeated measures (of the same DV on the same individuals) has been to use a multivariate model that treats those repeated measures as if they are distinct outcomes.

That is the context for my question to David Morse (or whoever else wants to jump in). I hope this clarifies things.

I also understand very well that any ANOVA model can be recast as a regression model. What I fail to see is how treating this particular problem as a regression model (rather than a RM ANOVA problem) will address the questions I have raised. Can you clarify that. Thanks.

And in case it is not clear, my questions are prompted by genuine curiosity. I do not profess great expertise in the area of multivariate statistics, and after reading Huberty & Morris (1989) and Huang (2020), I am not inclined to spend a lot of time trying to achieve expertise in MANOVA in particular! ;-)

Article Multivariate Analysis Versus Multiple Univariate Analyses

Article MANOVA: A Procedure Whose Time Has Passed?

Let me try to be more concise (and clearer) than I was in my previous post.

The suggestion that MANOVA requires distinct outcome variables would seem (to me) to rule out using MANOVA to analyze repeated measures designs. I am asking for clarification. Thanks to anyone who can offer it! ;-)

Bruce Weaver - thanks for the Huang paper (that'll save me writing my own "MANOVA sucks paper"!).

On the ANOVA issue I'd note that ANOVA can refer to:

1) an experimental design

2) a way of setting out SS in a table to decompose effects (used in many regression models - not just ANOVA)

3) a type of parameterisation of a regression model

4) a statistical model

I would argue that at least three of these remain useful even if you prefer to treat everything as a regression.

Hello all,

Well, if the original poster of the query hasn't been permanently frightened away from asking advice (the old joke: How do you get 13 different opinions? Ask a dozen economists for an answer), he's made of pretty stern stuff.

Here's the ideas underlying my answer.

0. I was intending neither to praise nor to bury a specific statistical procedure, or specific statistical software package.

1. High correlations among DVs do not negate the utility of manova (or discriminant analysis, in which case the IVs are the measures; or multivariate regression; or canonical correlation). I hope that part was understood.

2. The stature example I gave was one in which, barring a simple linear transformation, the only differences between scores on the two measures were due to measurement error. That's not what you want if you're trying to assert that the scores are different entities. As Bruce Weaver says, you certainly can make the method of quantification an IV in a model (as in repeated measures anova), but that type of thinking wasn't apparently part of the original query.

Some of the trade-offs between RM anova and manova are pretty well known: (a) the univariate method has better power for a given ES and N; (b) the assumption differences (sphericity when df > 1 for the RM dimension vs. equality of covariance matrices; univariate normality of model errors vs. multivariate normality) do mean that one evaluates model suitability in somewhat different ways; and (c) people often engage in less than informative follow-ups to a significant manova (e.g., forgetting the multivariate framework altogether, and reporting only univariate results). Again, that wasn't the question posed.

Be well, and best regards to the RGate community.

Thanks for your response, David Morse. Regarding your 2nd point above, I agree that making method of quantification an IV (so to speak) was not part of Guilherme Henrique Farias's original query.

@Bruce Weaver I apologies for my satirical post. I mean no disrespect to you or anyone else..I am trying to suggest that the use of the 1950 type ANOVA language.is detrimental to understanding statistics in the,2021 era. While many people were taught in that language.i notice that it is getting harder to get new students to see the relationship between sums of squares and modern regression Models. Sums of squares was about the ease of computation on Fisher's old desktop calculator. We no longer use those tricks to make computation more efficient

and they seemed to me to be more of a hindrance than a help. My own thoughts on this subject are still evolving so I am not always clear. I was suggesting for example that sphericity in ANOVA is more confusing because in the regression version it's handled more easily and in a less confusing manner. As an instructor I prefer that. I note that references to Andy Field's book are popular on this site. His statistics advice is confusing though his prose has won him awards. Reference here to Fields book are often confused and sometimes incorrect. I noticed the other day that a replay confused two goodness of fit tests and referenced Field. More modern language may tend to minimize such problems I hope.. Apologies again to you and to others I may have offended. . May we all be better in describing our methods. Your's in friendship, Best wishes, David Booth

No worries, David! ;-)