How do you find standard deviation for a paired difference test?

Question

How do you find the standard deviation for a paired difference test? 
My teacher provided an example related to this type of problem. The scenario involves working in Human Resources and assessing whether there is a difference in test scores after a training program. The sample consists of four pairs of scores: 
Before: 
- Sam: 85 
- Tamika: 94 
- Brian: 78 
- Mike: 87 
After: 
- Sam: 94 
- Tamika: 87 
- Brian: 79 
- Mike: 88 
The calculated standard deviation for this data set was 6.53. I already understand how to find the mean and degrees of freedom. Could someone please assist me in calculating the standard deviation? Thank you!

Anonymous · Accepted Answer

Before After   DifferenceSam         85      94           9Tamika    94      87          -7Brian       78      79           2Mike        87      88           1Mean difference = (9-7+2+1)/4 = 1.25Var =sum[(diff-mean diff)^2] / 3   = [(9-1.25)^2 + (-7-1.25)^2 + (2-1.25)^2 + (1-1.25)^2] / 3   = 128.75/3   = 42.92SD = sqrt(Var) = sqrt(42.92) = 6.55

Anonymous · Answer

Standard Deviation Of Differences

Arlo Bruen · Answer

This Site Might Help You.
RE:
How do you find standard deviation for a paired difference test?
My teacher gave an example for this kind of problem. The problem states that you work in Human Resources and you are trying to see if there is a difference in test scores after a training program. There are four pairs for the sample
               Before            After
Sam        85            …

Anonymous · Answer

Find The Sample Standard Deviation

Anonymous · Answer

A. √[(40-45.8)²+(38-45.8)²+(57-45.8)²+(53… /5 =√58.96… std= 7.67 B. √[(38-36.8)²+(34-36.8)²+(35-36.8)²+(45… /5 =√20.56… std= 4.53 I believe these to be the correct answers. It is hard to explain how to do it really, but I suggest you consult wikipedia if you want to know how to use the formula. Edit: err, it appears the poster above me got a different answer than I did. I am only in introductory stats, but still, I believe I did my answer correctly, especially because the internet has std solvers, and my answers checked. Edit again: Ya thats right, I remember hearing about that, but of course I forgot.. (so much to remember!). To Blahb: Nice catch on that, I would expect nothing less from a prof though ?

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How do you find standard deviation for a paired difference test?

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