# when "normalizing" values, do i need to re-calculate SEM

#### medstudent1

##### New Member
hello,

i apologize for the simple question, but i have no experience with stats. i have a data set that i am trying to analyze. i have calculated the mean and SEM. at this point i want to normalize all my means to a control. my question is do i have to re-calculate my SEM.

for instance

if i have

data set 1: 4, 4.2, 3.9, 4.7 -- mean of 4.2 and SEM of 0.177
data set 2: 0.5, 0.6, 0.7, 0.4 -- mean of 0.55 and SEM 0.0646

now i want to normalize my first set of data to the second. meaning i want to set my second set of data to a mean of 1....giving me the mean for my first set of 7.636. my question is what do i need to do to my SEM now?

thanks!!

#### Dragan

##### Super Moderator
meaning i want to set my second set of data to a mean of 1....giving me the mean for my first set of 7.636.
thanks!!

How did you get the mean of your first data set to be 7.636?

#### medstudent1

##### New Member
i should clarify...

the mean for my first set is 4.2 and the mean for my second is 0.55. i want to set the second set equal to 1 and hence adjust the first set accordingly.

so if 0.55 -> 1 then 4.2 -->7.636 = ((1/0.55)*4.2)

now how do i adjust the SEM - in the same way?

#### Dragan

##### Super Moderator
i should clarify...

the mean for my first set is 4.2 and the mean for my second is 0.55. i want to set the second set equal to 1 and hence adjust the first set accordingly.

so if 0.55 -> 1 then 4.2 -->7.636 = ((1/0.55)*4.2)

now how do i adjust the SEM - in the same way?
Okay, if you are taking each value from your first data set and dividing it by 0.55 (which is what I suspect your doing), then you would adjust the standard error as .177/.55 = .322.

Note: whenever you multipy a variable (X) by a constant (A) i.e. Y=A*X then the standard deviation of Y (SY) is:

SY = A*SX

where SX is the standard deviation of X. In your case A=1/.55. The standard error follows because all your doing is SEM=SY/Sqrt[N] (or SEM=SX/Sqrt[N]) where N is just a constant - the sample size.

#### medstudent1

##### New Member
Okay, if you are taking each value from your first data set and dividing it by 0.55 (which is what I suspect your doing), then you would adjust the standard error as .177/.55 = .322.

Note: whenever you multipy a variable (X) by a constant (A) i.e. Y=A*X then the standard deviation of Y (SY) is:

SY = A*SX

where SX is the standard deviation of X. In your case A=1/.55. The standard error follows because all your doing is SEM=SY/Sqrt[N] (or SEM=SX/Sqrt[N]) where N is just a constant - the sample size.
awesome. thank you very much!

#### NeuroscienceGal

##### New Member
This was very helpful for me as well, as I was having the same problem. However, I have a follow up question. If I now want to determine the statistical significance of the normalized samples using an unpaired student's t-test, how can I do this? I know how to normally run an unpaired-test for two groups. However, with the control group equal to 1, I have been unable to figure it out. Does the control group still have an SEM after setting it equal to 1? If so, how do you calculate that? If I still have an SEM for the control group, I could calculate the significance. Or is there a way to calculate it with an SEM? Thanks!