I am trying to normalize test data with its control. I have 3 independent values of "test data" and 3 independent values of "control data". I calculated mean and standard deviation for both independently. Now, I want to normalize the test data using the control. So, here I can have the normalized value of my test sample by dividing the "control mean value" from "test mean value" but what about the standard deviation? I think I need to use this STDEV values also for accurate normalization. How can I process this data?
A simple example to understand my question:
Test sample A has three values 3,4,5 and the control sample has three values 1,2,2. Now, the mean and standard deviation for Test sample is calculated as 4 and 1 respectively. In the same way, the mean and standard deviation for Control sample is calculated as 1.67 and 0.58 respectively. So, how can I normalize this Test data using the control data considering mean and std deviation.
see equation (3) in our paper: https://www.researchgate.net/publication/229218125_Improving_runoff_prediction_through_the_assimilation_of_the_ASCAT_soil_moisture_product
Being B the control sample:
A*=(A-mean(A))*std(B)/std(A)+mean(B)
Article Improving runoff prediction through the assimilation of the ...
Yogendra - It looks like the transformation Luca gave you is a z-value for each of the test data, times the standard error for the control sample, plus the mean of the control sample. His paper says it is to let the normalized values and the control values have the same mean and standard deviation. You get the mean of the control sample, plus z(A)*std(B), for each normalized point. Is that what you want for your application?
Or like says Jagddish you can use a log or similar transformation
indeed, you don't need to normalize your data. Our new paper would guide you
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
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