Date:         Mon, 12 Feb 2001 16:06:35 -0800
Reply-To:     Cassell.David@EPAMAIL.EPA.GOV
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "David L. Cassell" <Cassell.David@EPAMAIL.EPA.GOV>
Subject:      Re: Bartlett's test
Content-type: multipart/mixed;
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Christopher tong wrote:
> Is there a Bartlett's test for equality of variance (say,
> for residuals in an ANOVA model) in SAS v.8?

There is a Bartlett's test in the sample library.  If you don't have it

on your machine, you can get it from the SAS website [go to the tech
support
section and use the search facility].

HOWEVER.. that code computes the original Bartlett's test, which is highly
sensitive to departures from normality [see Box, 1953, Biometrika 40,
pp318-335].
There is a correction which helps this substantially, but I have not seen
any SAS code to do the computations.  So I went to the SAS website and
searched,
and found this:
                                                                           
                                                                           
                                                                           
                                                                           
  (Embedded image moved to file: pic00288.gif)  Is there a way to test for 
  homogeneity of variances/heteroscedasticity?                             
                                                                           
                                                                           
  Yes, It is also possible to model the variance at the same time that you 
  model the mean response using PROC GENMOD. Use the %VARMOD macro         
  available online.                                                        
                                                                           
                                                                           
  Bartlett's test can be done with the SAS/STAT Sample library program,    
  bartlett.sas (title: "Bartlett's Test for Homogeneity of Variance").     
                                                                           
                                                                           
  Beginning in Release 6.12, the MEANS statement in ANOVA and GLM includes 
  options for testing homogeneity of variances for one-way ANOVA models    
  and will perform Welch's test for differences between group means when   
  the group variances are not assumed to be equal. The Bartlett,           
  Brown-Forsythe, Levene, and O'Brien tests are provided.                  
  Example:  PROC GLM; CLASS TRT; MODEL Y=TRT;                              
            MEANS TRT/HOVTEST=LEVENE WELCH;                                
                                                                           
                                                                           
  Prior to Release 6.12, the %HOMOVAR macro performs the O'Brien,          
  Brown-Forysthe, Levine, Bartlett, and Welch Anova F tests for            
  homogeneity of variance. The macro requires base SAS and SAS/STAT        
  software (Release 6.06 or later). To use the %HOMOVAR macro, see the     
  documentation in the header or see the Proceedings of the Seventeenth    
  Annual SAS Users Group International Conference , 1992, pp. 1178-1182.   
  Or see the %VARMOD macro for additional information.                     
                                                                           



My personal preference would be Brown-Forsythe, since they don't do the

Fligner-Killeen test.  Levene appears to have a problem where "the type I
error rate sometimes becomes inflated to an unsatisfactory level".  That's
a quote from Conover, Johnson, and Johnson, 1981, Technometrics 23, pp
351-361.

HTH,
David
--
David Cassell, OAO Corp.                           Cassell.David@epa.gov
Senior computing specialist
mathematical statistician

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