Potential Limitations of ANOVA Testing

Date: 11/13/2005 at 14:59:06
From: Cathy
Subject: anova statistics

What is the DISADVANTAGE of the information reported by an ANOVA?

I can find all sorts of information about the results and use of 
ANOVA, but nothing on the disadvantage of the information the test 
reports.  According to my text book reference sources, it appears that
there are few (if any) disadvantages.

Date: 11/14/2005 at 11:42:25
From: Doctor Minter
Subject: Re: anova statistics

Hi Cathy!

The most distinct disadvantage to the analysis of variance (ANOVA) 
method is that it requires two assumptions to be made:

1.  All population means from each data group must be (roughly) equal.
2.  All variances from each data group must be (roughly) equal.

Obviously, we rarely have this luxury in real-world applications.  

There is light at the end of the tunnel, however, in the form of 
something called the Kruskal-Wallis Test, a non-parametric method that
will allow us to obtain a strong base to accept or reject the null 
hypothesis if these assumptions cannot be made.

If the assumptions are valid, however, ANOVA is unequivocally a 
powerful tool.

I hope this has shed some light on this method of statistics.  Please 
feel free to write again if you need further assistance, or if you 
have any other questions.  Thanks for using Dr. Math!

- Doctor Minter, The Math Forum
  http://mathforum.org/dr.math/