I have $10$ people in a group and they undergone a surgery. I have the root mean square of each subject before and after the surgery.

 Before     After
215.8231  105.7031
 35.0819   12.1916
 79.9559   32.8467
 75.0798   44.2913
 44.6203   18.8178
 21.207    16.5595
 56.8157   39.198
205.3445  110.0515
 39.8429   16.0174
116.1561   46.5451
 15.6692    9.5832

I would like to make these values to range between $0$-$1$. I used the formula $(\mathrm{value}-\min)/(\max-\min)$ for each group but it's not correct because I am loosing the information if the RMSE dropped down after the surgery.

Should I assume that my whole population is the Before and After and find the min value and max value?

What I did I found the min and max value before and then after and I normalised accordingly. I ended up with the following:

  Before       After
1            0.95671869
0.09698887   0.02596242
0.32118635   0.23155065
0.29682459   0.3454632
0.1446442    0.09191556
0.35341945   0.06943782
0.20557431   0.2947676
0.94764729   1
0.12077556   0.06404209
0.50204817   0.36789614
0            0

This way I don't know if the RMSE has been reduced.

Should I use $\min=9.5832$ and $\max=215.8231$ to the formula $(\mathrm{value}-\min)/(\max-\min)$ since those are the smallest and biggest numbers before and after? Would that be correct? I think I am loosing all the magnitude info this way but not sure how to work it out.

Any advice is greatly appreciated.

  • $\begingroup$ Why do you need to normalize the errors? $\endgroup$ – gunes Apr 1 at 11:53
  • $\begingroup$ I thought that will be better to present the error in values between 0-1. $\endgroup$ – Gina Apr 1 at 13:59

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