Roy's Largest Root

[Swetal Sindhvad]

Hello all,
I have run a MANOVA and the statistic Wilk's lamda for each of the
dependent variables shows that they do not have a significant effect
on the independent variables in my study. However, the statistic Roys
Largest Root shows significant interaction effects. How do I use this
statistic in my analysis? Does anyone have experience using Roys
Largest Root in their study?

Also, the SPSS output includes a note regarding Roys Largest Root for
the interactions that are significant...that note is:

"The statistic is an upper bound on F that yields a lower bound on the
significance level."

What does this mean? Is it possible that the interactions are not
significant after all?

Any help is greatly appreciated!

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[Kevin Bird]

Roy's Largest Root (RLR) test has important advantages over the multiple-root MANOVA test statistics when follow-up tests are to be based on the same critical value (of the test statistic used) as the initial overall test. See R.J. Harris' book A Primer iof Multivariate Statistics (preferably 2nd or 3rd edition) or Bird & Hadzi-Pavlovic (1983) Psychological Bulletin, 93, 167-178. "The statistic is an upper bound on F that yields a lower bound on the significance level" simply means that the p value obtained from the F approximation is too optimistic (ie it is inclined to say 'significant' much more often than it should). I have had cases of a quoted p (ie 'sig' in the output) of about .04, when the exact p is close to .4. Essentailly the F approximation is worthless (the Fs for the other test statistics are reasonable). You can obtain a near-exact p value from PSY (www.psy.unsw.edu.au/research/resources/psyprogram.html). You will need to know the values of three relevant parameters (see Harris, or run you data through SPSS MANOVA if so far you have used SPSS GLM), and you will need to know which of two versions of the RLR statistic you have in your output (the two SPSS programs give different versions) - again, see Harris. Incidentally, PSY uses 'theta' rather than 'lambda'.
 

Swetal Sindhvad wrote

Hello all,
I have run a MANOVA and the statistic Wilk's lamda for each of the
dependent variables shows that they do not have a significant effect
on the independent variables in my study. However, the statistic Roys
Largest Root shows significant interaction effects. How do I use this
statistic in my analysis? Does anyone have experience using Roys
Largest Root in their study?

Also, the SPSS output includes a note regarding Roys Largest Root for
the interactions that are significant...that note is:

"The statistic is an upper bound on F that yields a lower bound on the
significance level."

What does this mean? Is it possible that the interactions are not
significant after all?

Any help is greatly appreciated!

=====================
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[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