Recently I got sucked into meta analysis for two different research projects.
Unfortunately I am without references since I am traveling overseas.
Any help would be appreciated.
Here is a basic question.
Goal: A 95% confidence interval and t-test summarizing 5 sample means each with its own variance.
What I have so far:
The grand mean is the weighted average, with weights relative to sample sizes.
The variance the same using var(ax+by)=a^2var(x)+b^2var(y)
BUT should it be a t distribution with 4=5-1 degrees of freedom? Or would you use t-dist with N-1 degrees of freedom, where N=1049, the sum of the five sample sizes? Or should I be doing something else? Non parameteric? Maybe 5 studies isnt enough to conduct a good meta analysis? Ive had thoughts of running a bootstrap drawing from five t-distributions.
The overall effect is actually sorta borderline so it really does make a difference between p=0.03 and p=0.09, depending on which t-distribution I use. Im leaning towards the conservative df=4.