R help - Jun 2009 - ANOVA with means and SDs as input

Dear R-community,

I'm struggling with a paper that reports only fragmented results of a
2by2by3 experimental design. However, Means and SDs for all cells are given.

Does anyone know a package/function that helps computing an ANOVA with only
Means and SDs as input (resulting in some sort of effect size and
significance test)?

The reason why I'm interested is simple: I'm conducting a meta-analysis.
If
I included only what the authors would like to show the world, the results
would be somewhat biased...

I've combed through the web and my various books on R, but it's not that
easy to find. Or is it?

Thanks for your help!
Sebastian

On 25-Jun-09 10:15:30, Sebastian Stegmann wrote:
> Dear R-community,
> I'm struggling with a paper that reports only fragmented results
> of a 2by2by3 experimental design. However, Means and SDs for all
> cells are given.
> 
> Does anyone know a package/function that helps computing an ANOVA
> with only Means and SDs as input (resulting in some sort of effect
> size and significance test)?
No hope of that, unless you also have the numbers (N) of observations
in each cell (which of course may be equal across cells). You can get
a mean and an SD with anything from N=2 upwards.

If you do have the Ns, then one way is to construct an artificial
sample for each cell, such that the mean and the SD of each is equal
to the given mean and SD for the cell. Then you can submit the
resulting "reconstructed" data to a standard lm() in R. and carry
on from there.

The basic construct is:
Let a given cell have N data, mean=M, SD=S.

  X0 <- rnorm(N)
  X <- M + S*(X0 - mean(X0))/sd(X0)

Assuming you are going to do a standard normal ANOVA, the result
of operating with the above artificial data is algebraically the
same as if you had the true original data.

Hoping this helps!
Ted.
> The reason why I'm interested is simple: I'm conducting a
> meta-analysis. If I included only what the authors would like to
> show the world, the results would be somewhat biased...
> 
> I've combed through the web and my various books on R, but it's not
> that easy to find. Or is it?
> 
> Thanks for your help!
> Sebastian
--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 25-Jun-09                                       Time: 11:51:38
------------------------------ XFMail ------------------------------

Look at the anova.mean function in the HH package.
It does what you are asking, although limited to one-way ANOVA.

Le jeudi 25 juin 2009 ? 12:15 +0200, Sebastian Stegmann a ?crit
:
> Dear R-community,
> 
> I'm struggling with a paper that reports only fragmented results of a
> 2by2by3 experimental design. However, Means and SDs for all cells are
given.
> 
> Does anyone know a package/function that helps computing an ANOVA with only
> Means and SDs as input (resulting in some sort of effect size and
> significance test)?
> 
> The reason why I'm interested is simple: I'm conducting a
meta-analysis. If
> I included only what the authors would like to show the world, the results
> would be somewhat biased...
What you aim to do is not, as far as I can tell, possible using
already-programmed solutions in R packages. Some packages offer very
close solutions (e. g. lme()) but lack some necessary options (e. g. the
ability to fix intra-level variance in lme() : varFixed() works as
documented, not as what its name suggests...).

Why not use some established meta-analysis package such as meta or
rmeta ? You may have to recompute some variances or effect sizes, but it
can usually be done.

If you aim to go a bit farther (i. e. more than 2-groups comparisons),
the newly-released metafor package seems quite interesting. Wolfgang
Viechtbauer aimed to offer a tool for meta-regression, and the current
stage of the package (0.5.something IIRC) seems to be quite useable, if
somewhat counter-intuitive in places.

I'd recommend to have a look at it. WV didn't think useful to include
the vignettes and documentation for mima(), predecessor of metafor,
which explains quite nicely the motivation and algorithms he used. Too
bad... However, this documentation is still available on his Web site.
Be aware that the current "main interface" to the rma() function
(workhorse of the package) does not (yet ?) follow the usual format for
regression-like functions common to many R packages (the (formula, data,
subset, etc...) format). For example, you may make meta-regression, but
you'll have to code the model matrix yourself. Similarly, the necessary
bricks for (e. g.) indirect comparisons are here, but you'll have to
build them yourself (bring your wheelbarrow an some mortar...).

An alternative to be seriously considered : Bayesian modeling.
Meta-analysis is one of the rare medical domains where journal reviewers
won't immediately reject a paper at the sight of the B***sian word... As
far as I know, psychological journals are not as asinine. Here again,
some manual work will be in order. Some tutorial material is readily
available (google "Bayesian meta analysis tutorial", which should lead
you to the various "Statistics in Medicine" tutorials, among other
things).
> I've combed through the web and my various books on R, but it's not
that
> easy to find. Or is it?
Variance analysis through manual decomposition of sum of squares ?
Hugh ... I did that when I first learned anova(so long a time ago that I
am uncomfortable to think of it. In these times, even a pocket
calculator was too expensive for a random student (therefore forbidden
in exams), and I learned to cope with slide rule...). Tiring and messy.
Furthermore, "manual" algorithms (i. e. simple, non-iterative
algorithms) exists only for the simplest (e. g. one-way anova) or ideal
(e. g. balanced two-way anova with equal group sizes) cases ;
furthermore, modern critiques of the bases of such works cast some
doubts on their foundations (e. g. random- and mixed-effect anova)...

Therefore, the art is fast forgotten, if not totally lost. If you
insist, I might try to unearth my copy of Winer's handbook (ca. 1959)
and look up specific questions.

HTH,

					Emmanuel Charpentier