[R-meta] Question regarding aggregated SDs in meta-analysis

[Tzlil Shushan]

Hi everyone,

I wonder if someone would be kind and able to provide guidance/suggestions
on a stats issue that myself and colleagues are trying to handle while
performing a meta-analysis.

We are interested in the outcomes extracted from studies using football
games in which locomotor activity measures (collected using a global
positioning system) such as distances covered within fixed speed zones were
presented in different ranges. For example, mean and SD for 14–19.9 km/h,
and mean and SD for >20.0 km/h, separately for the same sample. We
considered to calculate an "overall exposure" measure (i.e. overall
distance >14 km/h) by simply aggregating the outcomes of the different
zones (i.e. the sum of the means), which is the main effect size in our
meta-analysis (using escalc “MN”). However, we are looking for the most
correct approach for calculating an aggregated/summed standard deviation as
a measure of dispersion across all zones.

We have found appropriate examples for the pooled standard deviation in
Cochrane handbook, for example here
https://handbook-5-1.cochrane.org/chapter_7/table_7_7_a_formulae_for_combining_groups.htm

However, as we aim to obtain the aggregated standard deviation it seems not
relevant to our case.

Building on the formula in above link, together with this one (equation 4
for equal sample size)

https://www.statisticshowto.com/pooled-standard-deviation/



We assume that we can sum the SD quadratically using the following formula
without dividing by the number of observations, means sqrt(sd1^2+sd2^2).



Such approach was mentioned in this thread:
https://stats.stackexchange.com/questions/25848/how-to-sum-a-standard-deviation







Does anyone have an idea whether we can use this formula for our aggregated
SD? We assume that this equation is relevant when assuming that the SDs are
independent, otherwise we have to add their covariance into the equation.
However, this information is not something that we can retrieve from
studies.



Thanks in advance,



Tzlil Shushan | Sport Scientist, Physical Preparation Coach

BEd Physical Education and Exercise Science
MSc Exercise Science - High Performance Sports: Strength &
Conditioning, CSCS
PhD Candidate Human Performance Science & Sports Analytics

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