John, I'm not an expert in meta-analysis but do have some familiarity
with it. I have a couple of points below:
(1) See the Wikipedia entry on Fisher's method for technical but brief
review of Stouffer's and Fisher's methods.
http://en.wikipedia.org/wiki/Fisher%27s_method#Relation_to_Stouffer.27s_Z-score_method
(2) Hunter and Schmidt (2004) in their "Methods of Meta-Analysis:
Correcting Error and Bias in Research Findings" has a section on
what they refer to as "cumulation of p-values across studies". They
point out that this is a method popularized by Rosenthal but (a)
when this method is used, effect size measures are reported along
with the p-values and Zs, and (b) there are a number of assumptions
that underlie the use of this method which lead H&S to say:
|...these methods are rarely used in the literature today.
They base this comments somewhat on the National Research Council's
recommendation that such methods not be used as well as their own
theoretical concerns (i.e., assumption of fixed-effects model for the
results instead of a random-effects model). H&S's book is on
books.google.com and the following link should bring you to about
page 448 (the method is covered on pp447-448 and elsewhere).
http://books.google.com/books?id=kImkui18i94C&printsec=frontcover&dq=hunter+schmidt+%22Methods+of+meta-analysis%22&hl=en&sa=X&ei=Rm0-Ucr7OayM0QHDw4CYCA&ved=0CDgQ6AEwAA#v=onepage&q=%22National%20research%20council%22&f=false
I would suggest that maybe you avoid the accumulation of p-values
method unless you have some real pressing reasons to use it.
At the very least, you should understand what sorts of criticisms
might be made to your analysis. And you really do have to provide
the effect sizes as well.
-Mike Palij
New York University
[email protected]
----------------- Original Message -------------------
On Mon, 11 Mar 2013 10:43:31 -0700, John Kulig wrote:
I am not the expert in meta-analysis, so any help will be appreciated. I am
currently finding some materials but in the meantime a few quick questions.
I know how to combine Z scores to get an overall Z and p level using
Stouffer's
methods - in my case I have 4 p values, and I would find the one-tail Z
corresponding to each p (using a negative Z IF the results were in the
opposite
direction). Adding the Z values and dividing by square root of the number of
studies yields a Z distribution. That I can do. But I have F and p values. F
distributions are chi2 ratios, positive, not normal .. etc. What would be
the
corresponding Z value for a p value greater than .5? It can't be a negative
Z.
I was toying with using Fisher's method for combining probabilities instead
...
-2*Sum log (p) which distributes as Chi square. I found very little info on
this method other than it gives similar but not identical results to
Stouffer.
I played with a few hypothetical numbers and ended up with quite different p
values in the end. Is that method still used? In the meantime I will start
plowing through a little book by Schultz on meta analysis ... Any help will
be
appreciated!
JK
p.s. I can also combine effect sizes across the studies, which I may do
later,
but, what I really want now is one overall "significance" level for these
quadratic trends ...
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