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 systematic review and meta-analysis.
In brief.... The outcomes extracted from the studies we detected as eligible are external load measures such as distances covered within fixed speed zones (e.g., 14-19.7 km/h, >19.8 km/h) and collected by using wearable devices (GPS systems). 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). However, we are looking for the most correct approach for calculating an aggregated/pooled standard deviation as a measure of dispersion across all zones. We have found three possible ways so far, with approach #1 for pooled standard deviation computation as suggested in the Cochrane handbook (link here: Cochrane handbook; approach #2 for pooled standard deviation computation for equal sample sizes; approach #3 for aggregated standard deviation computation for equal sample sizes. The three approaches return outputs which deviate from each other, and we are wondering what is the right approach for computing the SD of an aggregate composite score.
To contextualise and allow the community members to run a parallel simulation, I have attached a figure below with an example extracted from the dataset including the raw data, formulas and outputs of the simulation. The means and SDs refer to the outcomes covered in two different zones and collected from the same sample. For an easier replication, I attach the script of the formulas below:
Approach #1: SQRT(((B3-1)*E3^2+(B3-1)*E4^2+(B3*B3)/(B3+B3)*(D3^2+D4^2-(2*D3*D4)))/(B3+B3-1))
Approach #2: SQRT((D2^2+D3^2)/2)
Approach #3: SQRT(D2^2+D3^2)
Please note that the "overall exposure" outcome is a continuous variable, not normally distributed with a relatively strong right skew due to a predominant distribution of outcomes at the lower speed zones.
I have found useful info from a previous post here (How to 'sum' a standard deviation?, but it seems that the correct answer fitting our case was not completely clear or accepted.
I will appreciate comments or reference on this specific matter.
Antonio
