Date:         Tue, 6 Sep 2005 14:28:47 +1000
Reply-To:     Paul Ginns <p.ginns@itl.usyd.edu.au>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Paul Ginns <p.ginns@itl.usyd.edu.au>
Subject:      Re: About effect sizes
Content-Type: text/plain; charset="iso-8859-1"

Hi Karl,

a few suggestions for ANOVA effect sizes:

Cohen's f is one effect size you can use, but there are others. The standardised mean difference (Cohen's d) can be scaled up to factorial designs. Freeware which can be used to produce factorial d values, and confidence intervals around these d values, is available at http://www.psy.unsw.edu.au/research/PSY.htm and Kevin Bird has written a book about this approach to ANOVA called 

Bird, K.D. (2004). Analysis of variance via confidence intervals. London: Sage Publications. 

Note that the above webpage also includes some SPSS syntax for calculating studentized maximum root product interaction contrasts.

Another effect size is Epsilon squared. Jim Jaccard's Zumastat programme www.zumastat.com has a module that allows calcualtion of e-sq. and its CI using F values and degrees of freedom. (Note: I have no commercial interest in Zumastat.)

cheers,

Paul



Date:    Mon, 5 Sep 2005 16:27:02 +0200
From:    Karl Koch <TheRanger@gmx.net>
Subject: About Effect Sizes...

Hello group,

I have done a 3x3x2 factorial experiement which has significant main effects
and interactions. The DV was a score between 1 (not useful) and 6 (very
useful) on 6 levels. To know more about the magnitude of the three factors,
I was thinking of exploring the possibility to apply effect sizes. This
would also spice up the experiment documentation.

I found a, in my oppion good article in the Information Technology,
Learning, and Performance Journal which is available online
at:

http://education.nyu.edu/alt/beprogram/osrajournal/kotrlikwilliamsspring2003.pdf

The article states that for Analysis of Variance (which applies to me) I
should use Cohen's f effect size measure. Now my questions:

1) Can somebody here confirm that or does somebody here know other books or
articles (preferable also available online) which can help me to make a
decent decision on that? I know that the entire topic is pretty strong
discusses and some people disagree on what to choose. However, I am looking
for a decent narrative what to use. Some examples (papers?) where people
have used effect sizes in similar experiments would be helpful, too.

2) I have not only significant main effects but also significant
interactions. How does this influence the meaning of the effect size
measures of the meain effects.

3) If I want to find out the following: What is the most influcial factor
(the one that influenced the DV most) ? Can I use the effect size measure to
determine that e.g. by determining that by choosing the main effect with the
greatest effect size?

4) Is there any other way to rank the three factors according their
importance (in terms of influencing the DV by increasing the score)?

Any help would be greatly appreciated.

Kind Regards,
Karl