Tools for Those Who Summarize the Evidence Base
I'm new to meta-analytic techniques and am doing a meta-analysis on aging and divided attention. Specifically, I'm looking to see if age differences are larger for divided attention compared to full attention conditions. I'd like to calculate 2 effect sizes: one that is a standardized mean difference between young and old under full attention, and one that is a standardized mean difference between young and old under divided attention.
The problem that I'm running into is that some studies that I'd like to include report main effects and interactions without providing the means and standard deviations necessary to calculate the standardized mean differences. I know that if I have a one-way ANOVA or a t-test (e.g., comparing young and old under full attention conditions only) I could find the standardized mean difference, but what's possible to extract from a two-way ANOVA?
For example, let's say I have the results of a 2(age: young vs. old) x 2(attention: full vs. divided) ANOVA, and there's a main effect of age and no interaction. Could I use the F-statistic from the main effect to calculate a mean difference between young and old and use that for both the full attention and divided attention standardized mean differences? If the interaction were also significant, is there some way to calculate them? Would it be possible if I had the interaction effect plus the means but no standard deviations?
You need to use some little-known but quite important strategies to recreate the ANOVA summary table. We describe them in the appendix we have in our forthcoming chapter on meta-analysis (check here for a link to it; the link will expire around 16 September 2013; email me if you would like and the link no longer works).
If you have the means in the 2 x 2 design and any F value from the ANOVA in question, there are ways to determine the MSerror, the square root of which is an estimate of the pooled SD. Software I wrote a long time ago will do the math for you, it's described in the chapter. Hope that helps!