Comparisons in unbalanced nested-factor ANOVA

[Allan Lundy, PhD]

Dear Listers,
I've been very busy the last few months (that's the good news), so I haven't been an active responder for awhile (the bad news), but I'll participate more when I run out of work and/or retire.  Looking forward to the intellectual stimulation!

Meanwhile:  I have a client with a design in which varying numbers of individuals from different companies responded to a survey.  Different numbers of companies have been grouped into 3 industries.  The analysis concerns differences across industries.  Thus, companies are nested in industry.  An overall nested-factor ANOVA shows some differences across industry.  The question arises: are differences among the industries significant as predicted, as in Industry A scoring higher than B and C, but B and C industries do not differ?  This would be a straightforward planned comparison except that SPSS will not perform it with an unbalanced design (different numbers of companies nested in each industry). 

I have found some formulas for the correct MS error, but the symbols are specialized, so I am reluctant to assume that any given SPSS output would match it.  UNIANOVA's TEST subcommand looks like it might work if I could figure out the correct hypothesis term.  Would LMATRIX or KMATRIX work if CONTRAST does not?

Surely this problem must have arisen many times before.  Anybody know of syntax that would take care if it?

I was also thinking that I might get a pretty good approximation by reducing the comparison of interest to 2 groups (hence significance would show the effect I want)  This could be done by adding a level of nesting Comp, so that Comp would have two values: 0 assigned to Industry A, 1 to Industries B & C, then testing a "main effect" of Comp in:  company(industry(comp)).  This might lose some df but seems like it would give me what I want.  Also, would this be similar to simply lumping together Industries B & C and reducing it to a 2-group comparison?

Any thoughts?
Thanks!
Allan

Allan Lundy, PhD
Research Consulting
[hidden email]

Business & Cell (any time): 215-820-8100
Home (8am-10pm, 7 days/week): 215-885-5313
Address:  108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at www.dissertationconsulting.net ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

[Bruce Weaver]

Hello Allan.  I've only had a quick skim through your post, but this strikes me as a case for which I'd be using MIXED, not UNIANOVA.  If you are not familiar with multilevel models, you could take a look at Jos Twisk's nice introductory book--I found it extremely helpful in getting across the basic ideas, and preparing me to read some more advanced material.

HTH.

Cheers,
Bruce

Allan Lundy, PhD wrote

Dear Listers,
I've been very busy the last few months (that's the good news), so I
haven't been an active responder for awhile (the bad news), but I'll
participate more when I run out of work and/or retire.  Looking
forward to the intellectual stimulation!
Meanwhile:  I have a client with a design in which varying numbers
of individuals from different companies responded to a survey. 
Different numbers of companies have been grouped into 3 industries. 
The analysis concerns differences across industries.  Thus,
companies are nested in industry.  An overall nested-factor ANOVA
shows some differences across industry.  The question arises: are
differences among the industries significant as predicted, as in Industry
A scoring higher than B and C, but B and C industries do not
differ?  This would be a straightforward planned comparison except
that SPSS will not perform it with an unbalanced design (different
numbers of companies nested in each industry). 
I have found some formulas for the correct MS error, but the symbols are
specialized, so I am reluctant to assume that any given SPSS output would
match it.  UNIANOVA's TEST subcommand looks like it might work if I
could figure out the correct hypothesis term.  Would LMATRIX or
KMATRIX work if CONTRAST does not?
Surely this problem must have arisen many times before.  Anybody
know of syntax that would take care if it?
I was also thinking that I might get a pretty good approximation by
reducing the comparison of interest to 2 groups (hence significance would
show the effect I want)  This could be done by adding a level of
nesting Comp, so that Comp would have two values: 0 assigned to Industry
A, 1 to Industries B & C, then testing a "main effect" of
Comp in:  company(industry(comp)).  This might lose some df but
seems like it would give me what I want.  Also, would this be
similar to simply lumping together Industries B & C and reducing it
to a 2-group comparison?
Any thoughts?
Thanks!
Allan


Allan Lundy, PhD
Research Consulting
[e-mail]
Business & Cell (any time): 215-820-8100
Home (8am-10pm, 7 days/week): 215-885-5313
Address:  108 Cliff Terrace, Wyncote, PA 19095
Visit my Web site at

www.dissertationconsulting.net  


=====================
To manage your subscription to SPSSX-L, send a message to
[e-mail] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD