[R] ANOVA with means and SDs as input

[(Ted Harding)]

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

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Date: 25-Jun-09                                       Time: 11:51:38
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