Say we want to survey the literature to find out the effect of Treatment A on Value B.
Some studies provide an effect size estimate with confidence intervals and t-test results (e.g., “Treatment A had a significant effect on Value B (mean effect size = 3.5, 95% C.I. = [3, 4], p-value < 0.01”).
Other studies just provide the p-value from the t-test results (e.g., “Treatment A did not have a significant effect on Value B (p-value = 0.99)”).
How can the results from this second group of studies be included in a meta-analysis (if they can be included at all)?
Since there is no effect size given, I can’t really think of a way to include them. At the same time, to exclude them seems problematic (especially because it seems to me that the studies that find no significant effect are most likely to report the results in this way).
Right now my working solution is to keep track of this second group of studies, make a summary table regarding their conclusions, and present that along with the meta-analysis of the studies that do present effect size.
What are better solutions?
EDIT: Some clarification in response to a comment. Here are some examples of situations where effect size has not been presented.
Sometimes there are p-values.
Sometimes there are tables full of p-values.
But no effect sizes or raw data with which to calculate effect sizes. What's a person to do?