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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.

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Here is my current solution as described in the methods section:

We wrote a bootstrap program in R to obtain a confidence interval for the grand mean (6). We assumed that the five sampling distributions each had a student’s t-distribution centered at the reported point estimate and with the reported variance and with Nh-1 degrees of freedom. We re-sampled 2000 realizations from each of the five t-distributions and computed the grand mean (6) for each realization. The histogram (Figure 7) of these 2000 bootstrap realizations of the grand mean summarizes the results of the meta-analysis, and a 95% percentile confidence interval follows. The percentage of the bootstrap realizations of the grand mean greater than zero, gives an estimate of the Type I error for the point estimate estimate.
Here is my final effort on doing a meta-analysis:


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