effect sizes: generalized omega squared statistics

#1
hi all

i read this paper http://www.psych.umn.edu/courses/spring06/federicoc/psy8815/lectures/genomegasquared.pdf

and based on the following arguments:
1) very small sample size - needs unbiased estimation
2) repeated measures
3) 2 x 2 design

decided on reporting the generalized omega square (for repeated measures on pg 443) as my effect size statistic. i managed to figure out most of what they were referring to except for one tiny detail.

the problem is i am not very sure what they mean by "The quantity sigma^2 can be
estimated by the ratio of the pooled sum of squares for all sources of variance involving the subjects factor to the pooled degrees of freedom for these sources of variance. ... For a two-factor repeated measures design sigmaˆ2 = (SSs + SSsA + SsB + SSsAB )/(N − JK). Equation 7 is more convenient to use for calculating generalized omega squared. ..." (pg 443)

1) does SSs here refer to within or between subjects sum of squares?
2) SsB is a typo for SSsB right? SSsA, SSsB and SSsAB are the within subjects sum of square error in SPSS output yes?

I know that SSs within subjects sum of squares is not reported in SPSS output so i would have to calculate it on my own. for this, a friend suggested the following formula:

a x n x (Summation (mean score of subject across 4 conditions - mean score across subjects of mean score of subject across 4 conditions), where a and n refer to number of subjects and number of conditions respectively. i'm not sure that the definitions of a and n were correct... i thought it would just be the number of factors x number of levels. but my understanding of repeated measures is pretty fuzzy.

so i guess i have 2 questions regarding the repeated measures two factor generalized omega squared.
1) what is SSs referring to in the formula? and
2) how do i calculate it?

thanks in advance!

cheers
sam
 
#2
Hi Sam,

On your ANOVA output, look at the sums of squares attributed to 'Error' in both the Tests of Between-subjects Effects table AND the Tests of Within-subjects Effects table. Add all those together, then divide by the degrees of freedom associated with all those sums of squares. That gives you MSs/cells referred to in equation 7.

That's how I've been calculating it anyway. Hope it's right. I came across the same paper and decided generalised omega-squared would be the best effect size for the meta-analysis I'm doing for my research methods dissertation, so I've had to calculate quite a few of this effect size from different ANOVA tables now.

Hope this helps,
Marcus