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How to do paired t test with mean and sd?

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Rita on 29 Aug 2016
Commented: Aviram Shemen on 15 Aug 2020
I would like to do paired t-test with mean and standard deviation and the number of sampling.
for A:mean =8.37 sd=0.53
B: mean=8.18 sd=0.16 number of samples for both A=B=44


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Accepted Answer

Star Strider
Star Strider on 30 Aug 2016
To do it with only the means and standard deviations, you would have to write your own functions to calculate the one- and two-tailed t-probabilities, but fortunately with MATLAB that is not difficult:
Amean =8.37;
N = 44;
v = 2*N-2;
tval = (Amean-Bmean) / sqrt((Asd^2+Bsd^2)/N); % Calculate T-Statistic
tdist2T = @(t,v) (1-betainc(v/(v+t^2),v/2,0.5)); % 2-tailed t-distribution
tdist1T = @(t,v) 1-(1-tdist2T(t,v))/2; % 1-tailed t-distribution
tprob = 1-[tdist2T(tval,v) tdist1T(tval,v)]
tprob =
0.0253 0.01265
So your groups are significantly different at alpha = 0.05.
The functions are correct, but you may want to check my ‘v’ and ‘tval’ calculations to be certain it they are correct to your experimental design. If they are not, change them appropriately.


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Aviram Shemen
Aviram Shemen on 9 Aug 2020
Is there a way to do the paired t-test if I don't have the samples sizes?
(I'm trying to compare two results of a Cox regression model using coxphfit. So I have two means - exp(b1) and exp(b2) and two SE - se1 and se2)
Thanks in advance
Jeff Miller
Jeff Miller on 10 Aug 2020
This old answer is not correct for a paired t-test. In that case the tval computation depends on the standard deviation of the difference scores A-B. You can compute the required value from Asd and Bsd if you also have the correlation of A with B.

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More Answers (1)

Thorsten on 30 Aug 2016
Edited: Thorsten on 30 Aug 2016
If you have the Statistics Toolbox, you can use


Rita on 30 Aug 2016
Thanks a lot.I have this toolbox but can ttest function work with mean and sd without samples? Thanks again

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