[R-meta] Estimate variance from time series data
Arne Janssen
@rne@j@n@@en @ending from uv@@nl
Mon Aug 13 19:23:01 CEST 2018
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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