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I have data for 352 response ratings that have been categorized as "Low," "Medium," and "High." I would like to compare the differences of five variables across the three categories to see which ones have significant differences. In the end I would like to be able to say something like, "variable 1 differed significantly between the response categories, suggesting that it is an important component to consider..."

It seemed like a MANOVA was what I wanted to use for this, but the problem is that the sample sizes between the categories are quite different: "Low" = 66, "Medium"= 275, "High" = 11. Can I still use a MANOVA for this even with such a disparity? Any suggestions?

marzecovaa
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Anpanman
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    Why don't you drop the categorization and do a regression analysis? You would get rid of the unbalancedness and you would gain power, because categorization wastes information you have. Also MANOVA won't give you a result to interpret the way you want ("variable 1 differed..."). – Horst Grünbusch Aug 11 '14 at 14:32
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    Yes, you can. Different sample sizes *per se* are not a problem. However, with small sample size MANOVA (as any other statistical test) is likely to report no significant difference. See excellent answers [here](http://stats.stackexchange.com/questions/82705/unequal-sample-sizes-when-to-call-it-quits/82833#82833) and [here](http://stats.stackexchange.com/questions/31326/how-should-one-interpret-the-comparison-of-means-from-different-sample-sizes/31330#31330) about small sample sizes. – amoeba Jan 11 '15 at 19:44
  • You should have an adequate sample size. Although the larger your sample size, the better; for MANOVA, you need to have more cases in each group than the number of dependent variables you are analysing. – Dr Nisha Arora Mar 18 '16 at 08:17

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As in ANOVA, when cells in a factorial MANOVA have different sample sizes, the sum of squares for effect plus error does not equal the total sum of squares. This causes tests of main effects and interactions to be correlated. SPSS offers and adjustment for unequal sample sizes in MANOVA.

For further information have a look at: Tabachnick, B.G. and L.S. Fidell. 1996. Using Multivariate Statistics. Harper Collins College Publishers: New York.

Ferdi
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Martin IRYAYO
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