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What are the advantages of doing MANOVA of 2 response variables together rather than individual, separate analysis of response variables? What further information does it provide? Is it that the 2 sets of coefficients obtained from MANOVA are can be compared with each other and those from separate analysis cannot be?

For example in following example of a MANOVA: 

              num1    cat1     cat2     cat3     cat4       cat5    cat6   Residuals        
resp 1   112900.5   1128.4  19600.3  12087.9   2235.4     2484.0  11311.4  880808.9     
resp 2    19657.8   2408.9  12418.8  12593.0   7904.5     6684.0  20466.0  668647.0

P values for all of them are significant. Can we say that num1 and cat2 are more associated with resp1 while cat1, cat4 and cat6 are more related to resp2?

Coefficients from individual regressions are as follows:

for resp 1 (first response variable):

Residuals:
    Min      1Q  Median      3Q     Max 
-45.780  -7.218  -0.017   7.352  58.087 

Coefficients:
num1             1.32594  
cat1_level2     -0.83984  
cat2_level2     -0.69621  
cat2_level3      0.83189  
cat3_level2     -1.57992  
cat3_level3      1.29579  
cat4_level2      0.54523  
cat4_level3      0.28003  
cat5_level2      0.60691  
cat6_level2     -1.87730  
cat6_level3      0.80736

for resp 2 (second response variable):

Residuals:
    Min      1Q  Median      3Q     Max 
-45.780  -7.218  -0.017   7.352  58.087 

Coefficients:
num1             1.32594  
cat1_level2     -0.83984  
cat2_level2     -0.69621  
cat2_level3      0.83189  
cat3_level2     -1.57992  
cat3_level3      1.29579  
cat4_level2     -0.54523  
cat4_level3      0.28003  
cat5_level2      0.60691  
cat6_level2     -1.87730  
cat6_level3      0.80736

What would be the main advantage of MANOVA in this situation or others? Thanks for your insight.

ttnphns
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rnso
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  • I edited your title a bit. For the question itself, I recommend you to search the site: rather similar posts must have already appeared in the past. Univariate analyses can be helpful but they analyze marginal distributions and therefore answer not the same questions as multivariate methods do. – ttnphns Jun 06 '15 at 10:48
  • I tried to search but could not find a post with good explanation. – rnso Jun 06 '15 at 11:31
  • See e.g. [How can MANOVA report a significant difference when none of the univariate ANOVAs reaches significance?](http://stats.stackexchange.com/questions/129123) – amoeba Jun 06 '15 at 19:47

1 Answers1

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An answer is indeed not easily found.

MANOVA is more complicated than ANOVA, there are several ways to look at a MANOVA. It is possible to obtain significance in a two variable MANOVA while both the univariate tests are not. In this case a linear combination of the variables does separate the test groups. See sheet 9 of http://www.unt.edu/rss/class/mike/6810/MANOVA.pdf for the intuition; the pictures below are from that document.

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MANOVA can provide a more powerful test of significance than available when via univariate tests, this depends on the relationship between the variables thoug. This is only practical if the concept being tested is not strictly one-dimensional or univariate. An example being academic achievement, which might be defined as Maths, English, Science. This exampe is taken from http://en.wikiversity.org/wiki/Advanced_ANOVA/MANOVA, this page gives more information. Lumping variables to obtain significance is ofcourse not the idea.

spdrnl
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