# Error propagation problem

1. Nov 2, 2009

### xfshi2000

Hi all:
In magnetic resonance imaging such as human brain head image, I select several regions of interest (ROI) with the size of 8 pixel. Thus the average value and standard deviation are computed for each ROI. Now I want to evaluate the average value over different ROIs. For example, TotalAvg=[AvgVal(ROI1)+AvgVal(ROI2)+AvgVal(ROI3)]/3. How do I calculate the standard deviation of TotalAvg? It seems that If I use error propagation formula, it make no sense. Would anyone like to give one solution? Thanks

xf

2. Nov 2, 2009

### Bob S

The inverse variance (square of standard deviation) of the average value is the sum of the inverse variances of the individual ROIs. The variance is the square of the standard deviation. The ROI values you add should be weighted using their inverse variances. An ROI value with a small standard deviation has more weight than an ROI with a large one.

Se eqn(2) in
http://controls.engin.umich.edu/wik...ge,_standard_deviation,_z-scores,_and_p-value

Bob S

Last edited by a moderator: Apr 24, 2017
3. Nov 4, 2009

### xfshi2000

Thank you Bob. I got it.

xf