Calculating Standard Deviation After Normalizing Data

[verges_prime]

Ok, so I'm sure that I worded the topic of this thread poorly, but I'm a little lost as to exactly how to explain my problem. As such, I'll just lay out everyting in some detail and hope those of you with more stats expertise will understand )

The problem:

* I have data from 5 subjects

* Each subject gives 2 sets of data, 1 set is "pre-treatment" and the other "post-treatment"

* The "pre" and "post" data for all subjects cannot be lumped together in it's raw form, and it is not possible for me to take a mean and stdev over all subjects by just lumping all responses

* I have normalized the data for all subjects, and am now able to compare "post-treatment" responses across subjects. However, because that normalized data only takes into account the original mean value for each subject, and not the stdev of the raw data, I'm not sure how to compute the error bars for the normalized post-treatment responses. Any ideas?

* I would also (in a perfect world) like to be able to calculate an average response and stdev which lumps all subjects together. Can I calculate this from the normalized means I have now? How do I get the stdev for this value?

Thanks for taking the time to read through this. Any help would be appreciated.

 

[EnumaElish]

How did you normalize the data without taking account of the raw stdev?

 

[tacman]

First of all, it's great that you are taking the time to understand and analyze your data in a thorough manner. Let's break down the problem at hand:

1. You have data from 5 subjects, with 2 sets of data for each subject (pre-treatment and post-treatment).

2. You have normalized the data for all subjects, allowing you to compare post-treatment responses across subjects.

3. However, you are unsure of how to calculate the error bars for the normalized post-treatment responses because the normalized data does not take into account the standard deviation of the raw data.

4. You would also like to calculate an average response and standard deviation that lumps all subjects together.

To address the first issue, there are a few options that you can consider. One approach would be to calculate the standard deviation of the raw data for each subject separately, and then use those values to calculate the standard deviation of the normalized data. This would give you an estimate of the variability within each subject's data, which can then be used to calculate the error bars for the normalized post-treatment responses.

Another option would be to use a statistical software or tool that allows you to input raw data for each subject, and then calculates the standard deviation of the normalized data. This can be a more efficient approach, especially if you have a large amount of data.

As for your second question, it is possible to calculate an average response and standard deviation that lumps all subjects together from the normalized means you have now. To do this, you can simply take the mean of the normalized means for each subject, and then calculate the standard deviation of those values. This would give you an estimate of the average response and variability across all subjects.

In summary, it is important to take into account the standard deviation of the raw data when calculating the standard deviation of normalized data. Additionally, you can calculate an average response and standard deviation that lumps all subjects together by taking the mean of the normalized means and the standard deviation of those values. I hope this helps and good luck with your analysis!