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

In summary, the conversation discusses how to calculate the standard deviation of the average value of multiple regions of interest in a magnetic resonance imaging. It is mentioned that the inverse variance of the average value is the sum of the inverse variances of the individual ROIs, and the ROI values should be weighted accordingly. A link to a formula for calculating standard deviation is also provided.
  • #1
xfshi2000
31
0
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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  • #2
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:
  • #3
Thank you Bob. I got it.

xf
 

1. What is an error propagation problem?

An error propagation problem refers to the phenomenon where errors in the initial data or measurements used in a scientific experiment or calculation can lead to larger errors in the final result.

2. Why is error propagation important?

Error propagation is important because it allows scientists to understand and quantify the potential errors in their experiments or calculations. This helps ensure the accuracy and reliability of scientific findings.

3. How does error propagation occur?

Error propagation occurs when small errors in the initial data or measurements are amplified as they are used in calculations or experiments. This can happen through various mathematical operations or through the accumulation of multiple small errors.

4. How can error propagation be minimized?

Error propagation can be minimized by using precise and accurate measurement techniques, reducing sources of uncertainty, and using appropriate mathematical methods to account for errors. It is also important to repeat experiments and calculate average values to minimize the impact of random errors.

5. Can error propagation be completely eliminated?

No, error propagation cannot be completely eliminated, as all measurements and calculations have some degree of uncertainty. However, it can be minimized and managed through careful experimental design and data analysis.

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