[R-meta] Estimate variance from time series data

[Arne Janssen]

Dear list members,

I am doing a meta-analysis with data that are often presented as 
repeated measures of population densities, but authors sometimes also 
give overall averages and s.d. or s.e.. Because I want to combine these 
data into one analysis, I am interested in the overall effect size of 
the repeated measures, so would like to combine all data of the time 
series into one average and s.d. The time series are repeated several 
times, yielding data of the following form:
Time                Treatment 1                Treatment 2
                         N    Ave    s.d.                N    Ave    s.d.
1                      N1    x1,1    sd1,1          N2    x2,1    sd2,1
2                      N1    x1,2    sd1,2           n2    x2,2    sd2,2
...
...
...

What I want to obtain is one average and s.d. per treatment through time.
The average is straightforward, but I cannot come up with a calculation 
for the s.d.

The formula normally used for calculating the combined variance of two 
series of measurements:

Var = (s1^2(n1 -- 1) + s2^2(n2 -- 1) + n1(X-x1)^22 + n2(X-x2)^22)/( (n1 
+ n2 -- 1)

does not seem to apply when combining the measurements through time, 
because this increases the number of replicates, which in my opinion, 
should be the number of time series and not the number of observations.

I hope I made myself clear, and would be very grateful if you could 
advise me on this matter.

Thanks very much in advance.
Arne Janssen


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