How Do You Calculate the Standard Deviation of Total Average in MRI ROIs?

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SUMMARY

The calculation of the standard deviation of the total average in magnetic resonance imaging (MRI) involves using the inverse variance method. For regions of interest (ROIs) with computed average values and standard deviations, the total average is determined by summing the average values of the ROIs and dividing by the number of ROIs. The standard deviation of this total average is calculated by summing the inverse variances of the individual ROIs, where each ROI's value is weighted according to its inverse variance, emphasizing those with smaller standard deviations.

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  • Understanding of magnetic resonance imaging (MRI) concepts
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  • Study the inverse variance method for combining measurements
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Researchers and practitioners in medical imaging, particularly those working with MRI data analysis, statisticians, and anyone involved in quantitative assessments of regions of interest in imaging studies.

xfshi2000
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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
 
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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/wiki/index.php/Basic_statistics:_mean,_median,_average,_standard_deviation,_z-scores,_and_p-value

Bob S
 
Last edited by a moderator:
Thank you Bob. I got it.

xf
 

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